Dissertations / Theses on the topic 'Vacuum String Field Theory'

We study a quantum mechanical $\sigma$-model whose target space is a hyperKähler cone. As shown by Singleton, [184], such a theory has superconformal invariance under the algebra $\mathfrak{osp}(4^*|4)$. One can formally define a superconformal index that counts the short representations of the algebra. When the hyperKähler cone has a projective symplectic resolution, we define a regularised superconformal index. The index is defined as the equivariant Hirzebruch index of the Dolbeault cohomology of the resolution, hereafter referred to as the index. In many cases, the index can be explicitly calculated via localisation theorems. By limiting to zero the fugacities in the index corresponding to an isometry, one forms the index of the submanifold of the target space invariant under that isometry. There is a limit of the fugacities that gives the Hilbert series of the target space, and often there is another limit of the parameters that produces the Poincaré polynomial for $\mathbb C^\times$-equivariant Borel-Moore homology of the space. A natural class of hyperKähler cones are Nakajima quiver varieties. We compute the index of the $A$-type quiver varieties by making use of the fact that they are submanifolds of instanton moduli space invariant under an isometry. Every Nakajima quiver variety arises as the Higgs branch of a three dimensional $\mathcal N =4$ quiver gauge theory, or equivalently the Coulomb branch of the mirror dual theory. We show the equivalence between the descriptions of the Hilbert series of a line bundle on the ADHM quiver variety via localisation, and via Hanany's monopole formula. Finally, we study the action of the Poisson algebra of the coordinate ring on the Hilbert series of line bundles. We restrict to the case of looking at the Coulomb branch of balanced $ADE$-type quivers in a certain infinite rank limit. In this limit, the Poisson algebra is a semiclassical limit of the Yangian of $ADE$-type. The space of global sections of the line bundle is a graded representation of the Poisson algebra. We find that, as a representation, it is a tensor product of the space of holomorphic functions with a finite dimensional representation. This finite dimensional representation is a tensor product of two irreducible representations of the Yangian, defined by the choice of line bundle. We find a striking duality between the characters of these finite dimensional representations and the generating function for Poincaré polynomials.

This thesis discusses several aspects of string field theory. The first issue is bosonic open-closed string field theory and its associated algebraic structure -- the quantum open-closed homotopy algebra. We describe the quantum open-closed homotopy algebra in the framework of homotopy involutive Lie bialgebras, as a morphism from the loop homotopy Lie algebra of closed string to the involutive Lie bialgebra on the Hochschild complex of open strings. The formulation of the classical/quantum open-closed homotopy algebra in terms of a morphism from the closed string algebra to the open string Hochschild complex reveals deformation properties of closed strings on open string field theory. In particular, we show that inequivalent classical open string field theories are parametrized by closed string backgrounds up to gauge transformations. At the quantum level the correspondence is obstructed, but for other realizations such as the topological string, a non-trivial correspondence persists. Furthermore, we proof the decomposition theorem for the loop homotopy Lie algebra of closed string field theory, which implies uniqueness of closed string field theory on a fixed conformal background. Second, the construction of string field theory can be rephrased in terms of operads. In particular, we show that the formulation of string field theory splits into two parts: The first part is based solely on the moduli space of world sheets and ensures that the perturbative string amplitudes are recovered via Feynman rules. The second part requires a choice of background and determines the real string field theory vertices. Each of these parts can be described equivalently as a morphism between appropriate cyclic and modular operads, at the classical and quantum level respectively. The algebraic structure of string field theory is then encoded in the composition of these two morphisms. Finally, we outline the construction of type II superstring field theory. Specific features of the superstring are the appearance of Ramond punctures and the picture changing operators. The sewing in the Ramond sector requires an additional constraint on the state space of the world sheet conformal field theory, such that the associated symplectic structure is non-degenerate, at least on-shell. Moreover, we formulate an appropriate minimal area metric problem for type II world sheets, which can be utilized to sketch the construction of a consistent set of geometric vertices. The algebraic structure of type II superstring field theory is that of a $\mathcal{N}=1$ loop homotopy Lie algebra at the quantum level, and that of a $\mathcal{N}=1$ homotopy Lie algebra at the classical level.

In this thesis we consider some aspects of two dimensional Conformal Field Theory and their connection to String Theory. We have also studied some aspects of supersymmetry of M-Theory on Ricci-flat seven manifolds with 4-form fluxes. We concentrate mainly on certain supersymmetric extensions of the coset models due to Goddard, Kent and Olive (GKO). These models are known as the Kazama-Suzuki (KS) models and they are characterized by their N = 2 superconformal symmetry. Two series of the KS models enjoy a duality called level-rank duality which can be described roughly as duality between the dimension of the target space and the level of coset. We believe that the path-integral approach is the closest in spirit to string theory. Therefore, we formulate the level-rank duality of KS models in the path-integral approach by using the realization of GKO cosets as gauged Wess-Zumino-Novikov-Witten (gauged-WZNW) models. We derive, for a class of KS models, an expression for the partition function which is symmetric in the parameters of the level-rank duality. We compute the central charge of the models from this expression which matches that of Kazama and Suzuki in the operator approach. We then work out the target space metric and the dilation of the gauged-WZNW model based on the GKO coset SU(3)/(SU(2) x U(1)). It turns out to be quite a complicated metric with a non-trivial dilation. We verify, as a consistency check, that they satisfy the appropriate string theory effective equations of motion. We then argue that this background can arise naturally in type II string theory compactified down to AdS₃ space. We then turn to Eleven Dimensional Supergravity which is the low energy limit of M-theory. We adopt a metric ansatz which is a warped product of four dimensional Minkowski space and a (non-compact) seven manifold with 4-form fluxes turned on it. We derive the condition for unbroken supersymmetry with fluxes and non-trivial warp-factor. We show that the same condition implies that the seven manifold is conformal to a Ricci-flat manifold. We also point out the limitation of some naive ansatze about the structure of the Killing spinor. At this stage we are unable to give an explicit solution to the supersymmetry condition.

“Issues on tadpoles and vacuum redefinitions in String Theory” Marco Nicolosi Questa Tesi di dottorato è dedicata al problema dei “tadpoles” di NS-NS, funzioni ad un punto di campi bosonici assorbiti dal vuoto che tipicamente emergono nella Teoria delle Stringhe in seguito alla rottura della supersimmetria. Queste teorie contengono campi bosonici in due settori, quello di NS-NS e quello di R-R. Mentre i “tadpoles” di R-R tipicamente segnalano un’inconsistenza, come la presenza di anomalie quantistiche nel caso di spazi interni compatti, e quindi in generale devono essere cancellati, i “tadpoles” di NS-NS sono associati ad una ridefinizione del vuoto, come indicato per la prima volta da Fischler e Susskind negli anni ottanta. In particolare, nella stringa di Tipo I i “tadpoles” di NS-NS emergono già a livello del disco e, da un punto di vista spazio temporale, corrispondono a una configurazione di D-brane e piani di orientifold con tensione non nulla che danno luogo ad una netta attrazione gravitazionale che curva lo spazio tempo di “background”. Fino ad oggi siamo capaci di fare calcoli di stringa in maniera efficiente solo nel “background” piatto di Minkowski, un caso che è permesso e protetto dalla supersimmetria. Quindi, le divergenze infrarosse che emergono nelle ampiezze di stringa (canale chiuso) dopo la rottura della supersimmetria, dovute alla propagazione di stati non massivi di NS-NS che sono assorbiti dai “tadpoles” a impulso nullo, sono proprio il segnale che il “background” piatto di Minkowski non è più un vuoto della teoria. In questo contesto la nostra proposta è di continuare a quantizzare la stringa nel “background” di Minkowski e recuperare il risultato corretto risommando opportunamente i “tadpoles” in modo da cancellare le divergenze infrarosse. Questa procedura è comunque molto difficile da attuare nella Teoria delle Stringhe, perché le correzioni di “tadpoles” di ordine più grande corrispondono a superfici di Riemann di genere crescente, mentre si riescono a fare calcoli di stringa essenzialmente fino a genere uno (ampiezze ad un “loop”). Inoltre, nella maggior parte dei modelli che realizzano la rottura di supersimmetria, i “tadpoles” emergono già a livello del disco, e quindi, perfino in una regione perturbativa di piccola costante di accoppiamento di stringa, le prime correzioni di “tadpole” possono essere grandi. Pertanto, è interessante cercare modelli con “tadpoles” piccoli. Esempi di questo tipo sembrano essere forniti da modelli con opportuni flussi interni, per i quali risultati perturbativi credibili possono essere ottenuti considerando solo le prime correzioni di “tadpole”. Un’altra linea che si può perseguire è quella di cercare quantità che sono protette dalle divergenze infrarosse. Un esempio di questo tipo è dato dalle correzioni di stringa ad un “loop” alle costanti di accoppiamento di “gauge”, comunemente conosciute come “correzioni di soglia”, per modelli con supersimmetria rotta e con brane parallele, un caso che è stato ampiamente discusso in questa Tesi. Questa Tesi è organizzata nel seguente modo. Iniziamo con un’Introduzione generale sulla Teoria delle Stringhe, dove riportiamo le principale idee della Teoria, provando ad evidenziarne successi e problemi. Nel primo Capitolo richiamiamo le proprietà di base degli spettri di stringa e discutiamo qualche semplice esempio di compattificazione toroidale e di “orbifold”. Il secondo Capitolo è dedicato a riassumere differenti meccanismi di rottura di supersimmetria. Nel terzo Capitolo iniziamo ad analizzare il nostro programma di risommazione per diversi modelli giocattolo in Teoria dei Campi, provando a recuperare i giusti risultati, almeno a livello classico, a partire da un “vuoto sbagliato”. I casi di potenziale cubico e quartico sono semplici ed interessanti e mostrano alcune caratteristiche generali riguardanti le risommazioni dei “tadpoles” e i domini di convergenza intorno ai punti di flesso del potenziale, dove l’espansione nei “tadpoles” viene meno. La nostra analisi mostra che, partendo da un valore iniziale arbitrario del campo, la risommazione dei “tadpoles” a livello classico tipicamente guida le quantità che stiamo calcolando verso un estremo del potenziale, non necessariamente un minimo. Inoltre, nel caso del potenziale quartico troviamo alcuni punti molto speciali di “non-rinormalizzazione” per i quali tutte le correzioni di “tadpole” di ordine superiore si cancellano. Analizziamo poi la nostra procedura per un modello giocattolo inspirato dalla Teoria delle Stringhe, con “tadpoles” localizzati su D-brane di dimensione più bassa, calcolando le risommazioni esplicitamente. L’introduzione della gravità, che dovrebbe introdurre ulteriori complicazioni legate al termine di massa del gravitone, sembra non alterare sostanzialmente il nostro programma, ed infatti le risommazioni dei “tadpoles” continuano a funzionare ancora anche in questo caso. In fine, nel quarto Capitolo, iniziamo a trattare il problema dei “tadpoles” nella Teoria delle Stringhe. Nel primo Paragrafo, descriviamo un esempio dove la ridefinizione del vuoto può essere capita non solo a livello della teoria effettiva di bassa energia, ma anche a livello della stringa. In particolare, mostriamo che il vuoto di un “orientifold” di un modello di Tipo II con una dimensione compatta e “tadpoles” locali è un orientifold di Tipo 0 senza dimensioni compatte. Questi risultati sono contenuti in un articolo pubblicato in Nuclear Physics B. In fine, nell’ultimo Paragrafo, iniziamo l’analisi delle “correzioni di soglia” ad un “loop” in diversi modelli con rottura di supersimmetria e brane parallele, privi di tachioni chiusi che si propagano nel “bulk”. Il risultato è che le “correzioni di soglia” ad un “loop” in tutti questi casi sono sempre finite nell’infrarosso (canale chiuso), nonostante la presenza dei “tadpoles” di NS-NS. Questi risultati saranno inclusi in un articolo attualmente in preparazione.
“Issues on tadpoles and vacuum redefinitions in String Theory” M. Nicolosi This Thesis is devoted to the problem of NS-NS tadpoles, bosonic one-point functions going into the vacuum that typically emerge in String Theory after supersymmetry breaking. These theories contain bosonic fields in two sectors, commonly denoted with NS-NS and R-R. While R-R tadpoles typically signal an inconsistency, like the presence of quantum anomalies in the case of a compact internal space, and thus in general must be cancelled, NS-NS tadpoles are associated to redefinitions of the background, as first stressed by Fischler and Susskind in the eighties. In particular, in Type I String Theory NS-NS tadpoles emerge already at the disk level and, from a space-time viewpoint, correspond to configurations of D-branes and orientifold planes with a non-vanishing tension giving rise to a net gravitational attraction that curves the background space-time. Up to now one is able to perform efficient string computations only in a flat Minkowski background, a case that is allowed and protected by supersymmetry. Hence, the (closed) infrared divergences emerging after supersymmetry breaking in string amplitudes, due to the propagation of NS-NS massless states that are absorbed by tadpoles at vanishing momentum, are just the signal that the flat Minkowski background is no more a vacuum of the theory. In this context our proposal is to keep quantizing the string around the Minkowski background, recovering the proper results after suitable tadpole resummations that cancel the infrared divergences. This procedure is still very difficult to carry out in String Theory, because the higher-order tadpole corrections correspond to Riemann surfaces of increasing genus, and efficient calculations can be only carried out up to genus one (one-loop amplitudes). Moreover, in most models that realize supersymmetry breaking, tadpoles arise already at the disk level, and thus, even in a perturbative region of small string coupling, the first tadpole corrections can be large. Hence, it is interesting to search for models with “small” tadpoles. Examples of this kind seem are provided by models with suitable internal fluxes, for which reliable perturbative results can be recovered just considering the first tadpole corrections. Another line that one can pursue is to search for quantities that are protected against the infrared divergences. An example of this kind is provided by the one-loop string corrections to gauge couplings, commonly known as threshold corrections, for supersymmetry breaking models with parallel branes, a case that we have widely discussed in this Thesis. The Thesis is organized in the following way. There is a general Introduction to String Theory, where we summarize the main ideas of the Theory, trying to underline its successes and its open problems. Then in the first Chapter we recall the basic properties of string spectra and discuss some simple examples of toroidal and orbifold compactifications. The second Chapter is devoted to reviewing a number of different mechanisms to break supersymmetry. In the third Chapter we begin to analyze our resummation program in a number of field theory toy models, trying to recover the right results, at least at the classical level, starting from a “wrong vacuum”. The cases of cubic and quartic potentials are simple and interesting, and display some general features concerning tadpole resummations and convergence domains around inflection points of the potential, where the tadpole expansion breaks down. Our analysis shows that, starting from an arbitrary initial value of the field, classical tadpole resummations typically drive the quantities we are computing towards an extremum of the potential, not necessary a minimum. In addition, for the case of a quartic potential we find some very special “non-renormalization” points for which all higher order tadpole corrections cancel. We then analyze our procedure for a sting-inspired toy model with tadpoles localized on lower dimensional D-branes, performing explicitly the resummations. We also consider the introduction of gravity, that should give further complications related to the graviton mass terms, but seems to not affect substantially our program, and indeed tadpole resummations prove still to work in this case. Finally, in Chapter four we begin to face the tadpole problem in String Theory itself. In the first Section, we describe an example where the vacuum redefinition can be understood not only at the level of the low energy effective field theory, but also at the full string theory level. In particular, we show that the vacuum of a Type II orientifold with a compact dimension and local tadpoles is a Type 0 orientifold without compact dimensions. These results are contained in a paper to appear in Nuclear Physics B. Finally, in the last Section we begin the analysis of one-loop threshold corrections in a number of models with supersymmetry breaking with parallel branes and no closed tachyons propagating in the bulk. The result is that the one-loop threshold corrections in all these cases are always (closed) infrared finite, in spite of the presence of NS-NS tadpoles. These computations will be included in a paper that is currently in preparation.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
Includes bibliographical references (p. 115-127).
In this thesis we study the D-brane physics in the context of Witten's cubic string field theory. We compute first few terms the low energy effective action for the non-abelian gauge field A, from Witten's action. We show that after the appropriate field redefinition which relates the string field theory variables to the worldsheet variables one obtains the correct Born-Infeld terms. We then compute the rolling tachyon solution in the context of string field theory. We show that after the appropriate field redefinition we obtain the rolling tachyon solution of Sen.
by Ilya Sigalov.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2003.
Includes bibliographical references (p. 185-197).
In this thesis, we present some results that strongly support Sen's conjectures on tachyon condensation on a bosonic D-brane. Our main tool of analysis is level truncated open bosonic string field theory We use level truncation to check that the energy difference between the local maximum and the local minimum of the open bosonic tachyon effective potential is equal to the tension of a space-filling D-brane (Sen's first conjecture). Our results prove this equality within a precision of about 0.1%. We then construct lump solutions of open bosonic string field theory, which are conjectured by Sen (third conjecture) to be D-branes of lower dimensions. We check that indeed the tensions of lumps of codimension one and two, coincide with the tensions of the respective D-branes within a precision of a few percent. We also give evidence for Sen's second conjecture; that in the nonperturbative tachyon vacuum all open string degrees of freedom must disappear. We show that this is guaranteed if we can write the identity string field I in the form I = QA, where A is some string field and Q is the BRST operator in the true vacuum. We show evidence that the identity can indeed be written in this form. We also analyze the dynamics of tachyon condensation by studying time-dependent solutions of p-adic string theory and level truncated string field theory. Although our rolling solutions conserve energy, their pressure oscillates with diverging amplitudes. These results therefore don't support Sen's proposal of a pressureless tachyon matter.
by Nicolas Moeller.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
Includes bibliographical references (p. 77-81).
In this thesis we present some works done during my doctoral studies. These results focus on two directions. The first one is motivated by tachyon dynamics in open string theory. We calculate the stress tensors for the p-adic string model and for the pure tachyonic sector of open string field theory (OSFT). We give the energy density of lump solutions and attempt to evaluate the evolution of the pressure in rolling tachyon solutions. We discuss the relevance of the pressure calculation for the identification of the large time solution with a gas of closed strings. In the second direction, we give some results in closed string field theory (CSFT). We considered marginal deformations in CSFT. The marginal parameter, called a, is that associated with the dimension-zero primary operator cWcX&X. We use this marginal operator to test the quartic structure of CSFT and the feasibility of level expansion. We check the vanishing of the effective potential for a. In the level expansion the quartic terms generated by the cubic interactions must be canceled by the elementary quartic interaction of four marginal operators. We confirm this prediction, thus giving evidence that the sign, normalization, and region of integration Vo,4 for the quartic vertex are all correct.
(cont.) This is the first calculation of an elementary quartic amplitude for which there is an expectation that can be checked. We also extend the calculation to the case of the four marginal operators associated with two space coordinates. We then try to search a critical point of the tachyon potential in CSFT. We include the tachyon, the dilaton, and massive fields in the computation. Some evidence is found for the existence of a closed string tachyon vacuum. It seems that this critical point becomes more shallow when higher level contributions are considered. We also relate fields in the sigma model and those in CSFT. Moreover, large dilaton deformations are studied numerically. Finally, we use the low-energy effective field equations that couple gravity, the dilaton, and the bulk closed string tachyon to study the end result of the physical decay process associated with the instability of closed string tachyon. We establish that whenever the tachyon induces the rolling process, the Einstein metric undergoes collapse while the dilaton rolls to strong coupling. Some more general potentials and the possible cosmological application are discussed.
by Haitang Yang.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.
Includes bibliographical references (p. 133-142).
In this thesis I discuss various aspects of Witten's cubic string field theory. After a brief review of the basics of string field theory we begin by showing how string field theory can be used to check certain conjectures about the tachyon vacuum. We then discuss the problem of trying to globally gauge fix string field theory. We end with a discussion of various results in the quantization of the theory.
by Ian Thomas Ellwood.
Ph.D.

In this thesis we investigate astrophysical phenomena which arise in models with compact extra dimensions, focussing on the cosmological consequences of strings which wrap cycles in the internal space. Embedding our strings in the Klebanov-Strassler geometry we develop a concrete model of cosmic necklaces and investigate the formation of primordial black holes and dark matter relics from necklace collapse. Using data from the EGRET cosmic ray experiment, we place bounds on the parameters which de ne the warped deformed conifold, including the value of the warp factor and the radius of the compact space. Chapter 1 provides a brief overview, while background material is included in chapter 2, and these results are presented in chapter 3. In chapter 4 we analyse the dynamics of wound strings with angular momentum in the compact dimensions and determine the equation of motion for a self-oscillating loop. Finally, in chapter 5 we suggest a eld-theoretic dual for wound-string necklaces based on a modi cation of the standard Abelian-Higgs model. After introducing spatially-dependent couplings for the scalar and vector elds, we propose a static, non-cylindrically symmetric solution of the resulting eld equations which describes a \pinched" string with neighbouring vortex and anti-vortex regions. The similarities between pinched strings and the four-dimensional appearance of wound-string states are then examined and a correspondence between eld theory and string theory parameters is suggested. We nd that the topological winding number of the eld theory vortex may be expressed in terms of parameters which de ne the winding of the dual string around the compact space. According to this relation, the topological charge is equal to unity when the string has zero windings, and the standard Nielsen-Olesen duality is recovered in this limit. One key result of this work is an estimate of the Higgs boson mass (at critical coupling) in terms of the parameters which de ne the Klebanov-Strassler geometry and which, in principle, may be constrained by cosmological observations.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.
Includes bibliographical references (p. 245-262).
In this thesis, we present several works done in last three years. They include three directions in the string theory. In the first direction, we use the brane setup to find mirror pairs of SO(n) and Sp(k) gauge groups for N = 4 three-dimensional gauge field theories. To reach this result, we analyze carefully the s-configuration and predict a nontrivial string dynamics, i.e., the splitting of branes on the orientifold planes. In the second direction, we develop the "inverse algorithm" and use it to get nontrivial world volume theories of D-branes probing more exotic singularities. In this process, we find the "toric duality" which relates different phases of D-brane probe theories. We realize later that the toric duality is an example of the more powerful Seiberg-duality so these different phases are related by the Seiberg duality. In the third direction, by using numerical calculation we get a strong evidence to support the second conjecture of Sen's three conjectures. We show that if the identity field is BRST exact state around the tachyon vacuum, the open string spectrum will decouple from the physics and leave only the closed string spectrum.
by Bo Feng.
Ph.D.

Nach jahrelanger Suche hat sich bis heute Stringtheorie als einziger Kandidat einer konsistenten Quantentheorie der Gravitation herauskristallisiert. Um aus der Stringtheorie präzise Vorhersagen für unsere Niederenergiewelt zu gewinnen, ist es notwendig, das Vakuumproblem zu lösen, das heißt einen Mechanismus zu finden, der aufzeigt, in welchem Stringvakuum wir leben und warum die Natur dieses ausgewählt hat. Die Beantwortung dieser Frage benötigt nicht-perturbative Informationen.Diese wurden erst in jüngster Zeit zugänglich. Eine besondere Rolle in dieser Entwicklung spielten die sogenannten D-branes. Sie stellen mögliche nicht-perturbative Beiträge zu Stringamplituden dar. Die Identifizierung, daß D-branes einfach Objekte sind, auf denen Strings enden können, ermöglicht sie zu handhaben und zu zeigen, daß ihre Dynamik im wesentlichen durch Eichtheorien erfaßt wird. D-branes erlaubten, zahlreiche Dualit\ätssymmetrien zu etablieren, deren Haupta ussage zu sein scheint, daß alle 5 Stringtheorien sowie 11d Supergravitation nur verschiedene perturbative Limites einer fundamentalen 11d Theorie sind, T-Theorie. In dieser Arbeit habe ich mich mit einigen Anwendungen dieser Ideen beschäftigt. Die Tatsache, daß D-branes durch Super Yang-Mills Theorien beschrieben werden, erlaubt uns einen Stringhintergrund derart zu präparieren, daß wir nahezu jede Eichtheorie als relevante Niederenergiebeschreibung erhalten können. Eine besonders verbreitete Variante dieser Idee sind die sogenannten ``Hanany Witten setups'', in denen dieser Stringhintergrund nur aus flachen branes im flachen Raum besteht. Mit Hilfe dieser Technik habe ich verschiedene Dualitätssymmetrien in Feldtheorien auf Stringdualitäten zurückgeführt. Ferner ist es möglich, mit Hilfe der branes die Existenz nicht trivialer Fixpunkt Theorien in sechs Dimensionen zu beweisen und einige ihrer Eigenschaften zu analysieren. Einige dieser Fixpunkte beschreiben Phasenübergänge zwischen verschiedenen brane Hintergründen. Unter anderem läßt es sich auf diese Weise zeigen, daß es in 4 Dimensionen Übergänge zwischen chiralen und nicht chiralen Vacua gibt. Ferner wurde gezeigt, daß alle anderen Zugänge zu dem Problem, Eichtheorien in Stringtheorie einzubetten, im wesentlichen äquivalent zum HW Ansatz sind, in dem Sinn, daß die entsprechenden Stringhintergründe dual zueinander sind. Dadurch können neue Aspekte der String T-Dualität verstanden werden, so wie z.B. T-Dualitäat für brane Segmente und gebogene branes.Außerdem erlaubt uns diese Verbindung, die Phasenübergänge, die wir im HW Bild entdeckt haben, tatsächlich als Übergänge zwischen topologisch verschiedenen Stringkompaktifizierungen zu verst ehen.
In this thesis I discussed several applications of the connection of non-perturbative string theory and SYM theory. In Chapter 1 I reviewed the physics of D-branes as one example of a non-perturbative effect in string theory. Their dynamics is dominated by gauge theory. This fact can be used to engineer certain string backgrounds which yield interacting SYM theories as their low-energy description. In Chapter 2 I then introduced one of the approaches in detail, the HW setup. I gave a summary of the identification of the classical gauge theory, showed how quantum effects manifest themselves in the brane picture and how to solve them. This way of embedding gauge theories into string theories has several interesting applications. These were the topic of Chapter 3. First I discussed dualities in field theory and showed how they arise as a natural consequence of string duality. As a second application I used branes to prove the existence of non-trivial fixed point theories in 6 dimensions and to study their properties. Some of these fixed points describe phase transitions between two different brane configurations. From a 4d point of view these 6d transitions can induce a chiral non-chiral transition. In Chapter 4 I discussed the relation of the HW setup with the other approaches of embedding gauge theory into string theory, especially the branes as probes approach. The different ways of embedding gauge theories in string theory are shown to be actually T-dual as string backgrounds. For one this allowed us to explore several new aspects of T-duality, like T-duality for bended branes and branes endin g on branes. In addition this relation can be used to show that the transitions found in the brane picture can as well be understood as transitions between topologically distinct compactifications of string theory. Some open problems and directions for further research were mentioned in Chapter 5.

The study of solutions to open string field theory remains very much a work in progress, even for the bosonic string. In this dissertation I consider in detail two of these solutions involving marginal deformations of the original boundary conformal field theory. The first is a previously unknown solution in which two D-branes are translated before tachyon condensation occurs. This solution is studied in the level truncation scheme, in a sector which is larger than the universal subspace, but still less than the whole string Fock space due to several symmetries of the theory which take on a different content in the presence of two D-branes. This solution brings us a step closer to a full understanding of the relationship between the magnitude of a marginal deformation in BCFT and the strength of the corresponding marginal operator in OSFT. The other solution I study was first written down formally by Kiermaier and Okawa, and involves the renormalization of an exactly marginal operator. I consider the same solution with a more general renormalization scheme and find a set of sufficient restrictions for the solution’s validity. While this proceeds much as in the original work on this solution, I find some freedom in the solution as well as additional algebraic structure for renormalization schemes. I also present a collection of procedures written in Maple which define and manipulate wedge states with insertions, as well as computing correlation functions for such states provided that all inserted operators are sufficiently simple. Using this code I am able to calculate the tachyon profile of this solution for the time-symmetric rolling tachyon at 6th order in λ and describe its properties in comparison to previously known rolling tachyon profiles. I find the same unwanted oscillations that were seen in previous work on the time-asymmetric rolling tachyon.
Science, Faculty of
Physics and Astronomy, Department of
Graduate

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 179-185).
Open string field theory provides an action functional for open string fields, and it is thus a manifestly off-shell formulation of open string theory. The solutions to the equation of motion of open string field theory are expected to describe consistent classical open string backgrounds. In this thesis, I present a number of analytic results in bosonic open string field theory. Firstly, I present analytic solutions to the equation of motion that describe an exactly marginal deformation of the chosen open string background. A prominent example in this class is the rolling-tachyon solution, which describes the decay of an unstable D-brane. Furthermore, I demonstrate that the Riemann surface geometry of string perturbation theory can be radically simplified using propagators of Schnabl gauge instead of Siegel gauge. In principle, this simplification allows the analytic computation of arbitrary off-shell one-loop open string amplitudes. Finally, I show that this simplicity of Schnabl gauge one-loop Riemann surfaces can be combined with the knowledge of analytic solutions to construct an analytically computable string field theory boundary state. For all known solutions, this boundary state precisely coincides with the BCFT boundary state of the open string background that the solution is expected to describe. This construction thus confirms the physical interpretation of known analytic solutions and thus provides a nice consistency check on open string field theory.
by Michael Stefan Kiermaier.
Ph.D.

In Chapter 1, we give an introduction to the topic of open string field theory. The concepts presented include gauge invariance, tachyon condensation, as well as the star product.

In Chapter 2, we give a brief review of vacuum string field theory (VSFT), an approach to open string field theory around the stable vacuum of the tachyon. We discuss the sliver state explaining its role as projector in the space of half-string basis. We review the construction of D-brane solutions in vacuum string field theory. We show that in the sliver basis the star product correspond to a matrix product.

Using the material introduced in the previous chapters, in Chapter 3 we establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, we show that (off--shell) level--matched closed string states are represented by star algebra projectors in open string field theory. As an outcome of our identification, we show that boundary states, which in closed string theory represent D-branes, correspond to the identity string field in the open string side.

We then turn to noncommutative field theories. In Chapter 4, we introduce the framework in which we will work. The tools introduced are solitons, projectors, and partial isometries.

The ideas of Chapter 4 are applied to specific examples in Chapter 5, where we present new solutions of noncommutative gauge theories in which coincident vortices expand into circular shells. As the theories are noncommutative, the naive definition of the locations of the vortices and shells is gauge-dependent, and so we define and calculate the profiles of these solutions using the gauge-invariant noncommutative Wilson lines introduced by Gross and Nekrasov. We find that charge 2 vortex solutions are characterized by two positions and a single nonnegative real number, which we demonstrate is the radius of the shell. We find that the radius is identically zero in all 2-dimensional solutions. If one considers solutions that depend on an additional commutative direction, then there are time-dependent solutions in which the radius oscillates, resembling a braneworld description of a cyclic universe. There are also smooth BIon-like space-dependent solutions in which the shell expands to infinity, describing a vortex ending on a domain wall.

In Chapter 6, we review the Fronsdal models for free high-spin fields that exhibit peculiar properties. We discuss the triplet structure of totally symmetric tensors of the free String Field Theory and their generalization to AdS background.

In Chapter 7, in the context of massless higher spin gauge fields in constant curvature spaces discussed in chapter 6, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and the angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.

Doctorat en Sciences
info:eu-repo/semantics/nonPublished

The time evolution operator of quantum field theory (Schrödinger functional) can be written in terms of particles moving on S(^1)/Z(_2-). By deriving the 'gluing property’ which joins two propagators across fixed time surfaces, we show that the Feynman diagram expansion of the free Schrödinger functional is determined once we know the field propagator. We generalise the gluing property to a new method of sewing string field propagators and construct the string field Schrödinger functional in terms of strings moving on S(^1)/Z(_2-). Timelike T-duality in string theory then appears as a large/small time symmetry of string field theory with an exchange of boundary states and string backgrounds. All of our arguments apply equally to the open and closed string. The addition of interactions to quantum field theory bring no complication to our arguments, but modifications are required when the interaction is non-local. As application of these methods we construct the interacting string field vacuum wave functional using knowledge of the vacuum expectation values it must generate.

Die physikalischen Kräfte in der Natur werden durch zwei fundamentale Theorien be- schrieben: Das Standard Modell der Elementarteilchenphysik kann die Wechselwirkun- gen zwischen Elementarteilchen, also die Physik auf mikroskopischer Skala, erklären. Das Gegenstück ist die allgemeine Relativitätstheorie, die die Physik auf makrokopischen, kosmologischen Skalen widergibt. Eine fundamentale Frage an die theoretische Physik ist es, diese beiden Theorien zu vereinigen. String Theorie ist ein Kandidat für eine solche vereinheitlichende Theorie. In den letzten Jahren wurden große Fortschritte auf diesem Gebiet erzielt. Zum ersten Mal wurde es möglich, in den starken Kopplungsbereich vorzudringen. Das Mittel, das hier benutzt wird, sind die sogenannten Dualitätssymmetrien, die den starken Kopplungs- bereich einer Theorie in den schwachen Kopplungsbereich einer anderen Theorie abbilden. Man glaubt, daß letztendlich die bekannten konsistenten Stringtheorien lediglich unter- schiedliche perturbative Limites einer fundamentalen Theorie, der M- oder F-Theorie, sind. Außerdem wurde klar, daß Stringtheorien nicht nur eindimensional ausgedehnte Objekte, die Strings, enthalten, sondern auch höherdimensionale "Branen". Die Masse dieser Objekte ist bei schwacher Stringkopplung sehr groß, bei starker Kopplung geht ihre Masse hingegen gegen 0. Dualitätssymmetrien können Strings und höherdimensionale Branen in Beziehung setzen. Diese Arbeit ist einigen Anwendungen der Branen gewidmet. Im Niederenergielimes ist die Weltvolumentheorie solcher Branen durch eine Feldtheorie gegeben. Dies wird benutzt, um Eigenschaften von Feldtheorien im Stringtheorie-Kontext zu reproduzieren. In Kapitel 2 verwenden wir bestimmte Konfigurationen von sich im Raum schneidenden Branen, um Theorien mit (0; 1) Supersymmetrie in sechs Dimensionen zu studieren. Von der Feldtheorieseite her ergibt sich die Anomaliefreiheit als Konsistenzbedingung an chirale Theorien. Diese Bedingung kann in der String-Theorie als Ladungserhaltung von dort auftretenden Eichpotentialen reproduziert werden, d.h. als eine Konsistenzbedingung an die möglichen Branenkonfigurationen. Das Kapitel 3 beschäftigt sich mit Matrix-Modellen. Hierbei handelt es sich um einen Vorschlag, wie die fundamentale M-Theorie formuliert werden könnte. M-Theorie in der Lichtkegel-Eichung soll durch ein quantenmechanisches Modell erfaßt werden. Die Kompaktifizierungen von M-Theorie werden durch niederdimensionale Feldtheorien beschrieben, die wiederum als Feldtheorien auf Branen interpretiert werden können. Wir befassen uns mit der Kompaktifizierung von Matrix-Theorien auf Tori und diskutieren hierbei insbeson- dere Probleme, die bei Kompaktifizierungen auf sechs dimensionalen Tori auftreten. Hier scheint es { anders als für niederdimensionalere Tori und genau wie für höherdimensionale Tori { keine Beschreibung als niederdimensionale Feldtheorie zu geben. Das letzte Kapitel behandelt die Kompaktifizierung von M- bzw F-Theorie auf Calabi- Yau 4-Mannigfaltigkeiten. Dies führt auf den phänomenologisch relevanten Fall von N = 1 Supersymmetrie in vier Dimensionen. Es wird gezeigt, daß topologisch ver- schiedene Calabi-Yau Mannigfaltigkeiten durch Übergänge über singuläre Konfiguratio- nen verbunden werden können. Die Vakua, die durch Kompaktifizierung auf den durch die Singularität verbundenen Mannigfaltigkeiten erhalten werden, haben physikalisch un- terschiedliche Eigenschaften. So können gewisse Divisoren, die durch Ausglätten der Singularität entstehen, zur Folge haben, daß ein nicht-perturbatives Superpotential durch Branen erzeugt wird, die sich um die betreffenden Divisoren herumwickeln.

This thesis is divided into two parts. The first part concerns the study of the ambitwistor string and the scattering equations, while the second concerns the interplay of the symmetries of the asymptotic null boundary of Minkowski space, called [scri], and scattering amplitudes. The first part begins with a review of the CHY formulas for scattering amplitudes, the scattering equations and the ambitwistor string including its pure spinor version. Next are the results of this thesis concerning these topics, they are: generalizing the ambitwistor model to higher genus surfaces; calculating the one-loop NS-NS scattering amplitudes and studying their modular and factorization properties; deriving the one-loop scattering equations and analyzing their factorization; showing that, in the case of the four graviton amplitude, the ambitwistor amplitude gives the expected kinematical prefactor; matching this amplitude to the field theory expectation in a particular kinematical regime; solving the one loop scattering equations in this kinematical regime; a conjecture for the IR behaviour of the one-loop ambitwistor integrand; computing the four graviton, two-loop amplitude using pure spinors; showing that this two-loop amplitude has the correct kinematical prefactor and factorizes as expected for a field theory amplitude; generalizing the ambitwistor string to curved backgrounds; obtaining the field equations for type II supergravity as anomaly cancellation on the worldsheet; generalizing the scattering equations for curved backgrounds. The second part begins with a review of the definition of the null asymptotic boundary of four dimensional Minkowski space, its symmetry algebra, and their relation to soft particles in the S-matrix. Next are the results of this thesis concerning these topics, they are: constructing two models consisting of maps from a worldsheet to [scri], one containing the spectrum of N=8 supergravity, and the other the spectrum of N=4 super Yang-Mills; showing how certain correlators in these theories calculate the tree-level S-matrix of N=8 sugra and N=4 sYM respectively; defining worldsheet charges which encode the action of the appropriate asymptotic symmetry algebra and showing that their Ward-identities recover the soft graviton, and soft gluon factors; defining worldsheet charges for proposed extensions of these symmetry algebras and showing that their Ward-identities give the subleading soft graviton and subleading soft gluon factors.

The cosmological constant appearing in Einstein’s equations is a key element of the ΛCDM standard cosmological model. This term performs, effectively, as pure vacuum energy, and is considered the easiest explanation of the positive acceleration of the current Universe. But despite the successes of the concordance model in explaining a large variety of high precision data, some tensions are also present at the observational level, and there are also some important problems arising on the theoretical side. The most severe one is the so-called “cosmological constant problem”, which is caused by the gigantic discrepancy between the predicted value of the vacuum energy density in Quantum Field Theory and the measured one. This huge difference is considered as one of the most profound (unsolved) problems of theoretical Physics and its solution probably will come hand in hand with a change of paradigm. But at this moment, there is no clear hint pointing to the aforesaid solution. In view of the current status of the problem, those phenomenological studies that are able to shed some light on the nature of the dark energy (DE) component that is dominating the current Universe, are very welcome. In this thesis are presented detailed studies (at the background and perturbations levels) on various running vacuum energy models, which are motivated from the renormalization group equation formalism of Quantum Field Theory in curved spacetime. In these models, the cosmological term is not a rigid Λ, it depends explicitly on the Hubble function and its time derivative. Thus, it varies with the cosmic expansion. Upon the study of the capability of these models on fitting the experimental data, we can determine whether this dynamical behavior is favored by observations or not. Is the vacuum energy density (or in more general terms, the dark energy density) dynamical? One of the main conclusions of this dissertation is that we have indeed strong evidences in favor of the variability of the DE throughout the cosmic history. It has been shown that this variation can also be traced through other (purely phenomenological) dynamical vacuum models, together with different parameterizations of the DE (as the XCDM and CPL), and scalar field models as the Peebles-Ratra one. The statistical confidence level with which these evidences are obtained reaches in some cases the 4σ c.l., something that is unprecedented in the literature. An exhaustive explanation on the reasons why large collaborations as BOSS or Planck have not been able to detect such signal in favor of the DE dynamics is provided in this thesis too. This is mainly due to the fact that they do not make use of a complete enough data set that include more large scale structure (LSS) and baryon acoustic oscillations (BAO’s) data points. The analyses carried out in this thesis have also served e.g. for: 1) ruling out some running vacuum models (and DE models inside the D-class) without a well-defined ΛCDM limit (with no constant term in the expression for the vacuum energy density); 2) showing the potential of the Press-Schechter formalism in the characterization of the various vacuum models; 3) pinpointing the importance of the data set BAO+CMB+LSS in front of other data sets as those formed by Hubble function data points and the luminosity distance versus redshift points of type Ia supernovae.
La constant cosmològica és un element clau del model ΛCDM, el model estàndard cosmològic. Aquest terme actua, de manera efectiva, com energia pura de buit, i representa l’explicació més senzilla de l’acceleració positiva amb la que s’expandeix l’Univers actualment. Ara bé, tot i que el model estàndard cosmològic és capaç de desciure dades observacionals provinents de fonts molt diverses amb molta precisió, es coneixen també algunes tensions a nivell observacional, així com també greus problemes teòrics associats. El més sever és el que es coneix com el “problema de la constant cosmològica” i té a veure amb la gran diferència (de més de 55 ordres de magnitud) entre l’estimació teòrica de la densitat d’energia de buit que es fa a partir de la Teoria Quàntica de Camps i el valor mesurat de la mateixa. Aquesta discrepància és exageradament gran i representa un dels problemes més importants de la Física teòrica actual. Ara per ara, no sembla que disposem de les eines teòriques per solucionar aquest problema. En aquest sentit, estudis fenomenològics que puguin ajudar a caracteritzar millor l’energia fosca que domina l’expansió del teixit còsmic són molt benvinguts. En aquesta tesi es recullen els estudis detallats (a nivell de background i pertorbacions) de diferents models de buit dinàmic que neixen del formalisme del grup de renormalització en Teoria Quàntica de Camps en espais corbats. En aquests models, el terme cosmològic no es pren constant, sinó com una funció explítica de la funció de Hubble i la seva derivada. Per tant, la densitat d’energia de buit varia amb l’expansió de l’Univers. Estudiant la capacitat d’aquests models per ajustar les dades experimentals podem veure si realment la dinàmica d’aquesta component còsmica està o no afavorida per les observacions. És la densitat d’energia de buit (o, en termes més generals, la densitat d’energia fosca) dinàmica? Una de les conclusions més importants a les que s’arriba en aquesta dissertació és que hi ha indicis grans a favor d’aquesta variabilitat de l’energia fosca en el temps i que aquesta pot ser traçada també a partir d’altres models de buit dinàmic purament fenomenològics, així com amb diverses parametritzacions de l’energia fosca (com la XCDM o CPL) i models de camps escalars com el de Peebles- Ratra. El nivell trobat d’evidència a favor d’aquesta dinàmica no nul·la no té precedents a la literatura, arribant en alguns casos a les 4σ de nivell de confiança.

Die Arbeit beschäftigt sich mit zwei Themen: den nichtkommutativen Yang-Mills-Theorien und der AdS/CFT-Korrespondenz. Im ersten Teil wird eine teilweise Aufsummation der theta-entwickelten Störungstheorie untersucht. Letztere stellt einen Weg dar, nichtkommutative Yang-Mills-Theorien mit beliebigen Eichgruppen G als Störungsentwicklung im Nichtkommutativitätsparameter theta zu definieren. Es wird gezeigt, daß man im Fall, daß G eine echte Untergruppe von U(N) ist, die ungleich einer U(M) ist (M
This thesis addresses two topics: noncommutative Yang-Mills theories and the AdS/CFT correspondence. In the first part we study a partial summation of the theta-expanded perturbation theory. The latter allows one to define noncommutative Yang-Mills theories with arbitrary gauge groups G as a perturbation expansion in the noncommutativity parameter theta. We show that for G being a subset of U(N) but not equal to U(M), M

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 185-194).
In this thesis, we use string theory constructions and dualities to explore various features of interacting quantum field theories. We begin with an overview in Chapter 1, of past and recent developments in quantum field theories, explaining the advantages of string theoretic techniques over traditional approaches in answering a range of questions about interacting dynamics. In Chapter 2 we study the holographic duality between the 6d (1, 1) Ak-1 little string theory (LST) and type II string theory in the double scaled limit. By identifying the low energy states, which are Cartan gluons in the 6d maximal super-Yang-Mills (SYM) that describes the massless sector of the LST, we compute the four-point amplitudes from both sides of the duality and demonstrate matching results. Since the two computations concern different regimes in the parameter space, their amazing agreement implies the presence of certain nonrenormalization theorems in the 6d SYM. In Chapter 3, motivated by the AdS/CFT duality, we develop a systematic procedure to derive an off-shell action for hydrodynamics from classical Einstein gravity. We first identity the boundary fluid degrees of freedom in the hydrodynamic regime, in terms of gapless modes of the metric in the bulk gravity. This allows us to derive an off-shell action, for relativistic fluids that have gravity duals, at leading order in derivative expansion, by explicitly integrating out gapped degrees of freedom in the bulk. We also explain the strategy to incorporate dissipation and higher order effects. In Chapter 4, we discuss 4d N = 2 superconformal field theories (SCFT) of the Argyres-Douglas (AD) type, which can be constructed in string/M theory by either wrapping M5 branes on punctured Riemann surface or probing 3-fold singularity by IIB string. We classify the punctures (irregular defects in Hitchin system) on the Riemann surface in the former construction, that will give rise to N = 2 SCFTs and demonstrate how to extract exact information about the Coulomb branch spectrum and central charges. We further identify these AD theories constructed from M5 branes with a special class of theories from IIB probing compound Du Val (cDV) singularities, thereby establishing a mathematical connection between singular Hitchin systems and cDV singularities through N = 2 SCFTs. We end with a short summary and outlook for future directions in Chapter 5.
by Yifan Wang.
Ph. D.

In dieser Dissertation werden Aspekte von superkonformen Quantenfeldtheorien untersucht, die für die sogenannte AdS/CFT Korrespondenz relevant sind. Die AdS/CFT Korrespondenz beschreibt eine Dualität zwischen Stringtheorien im Anti-de Sitter Raum und superkonformen Quantenfeldtheorien im Minkowskiraum. In diesem Kontext wurde die sog. Wilsonschleifen / Amplituden Dualität entdeckt, die die Übereinstimmung von n-Gluon MHV Amplituden und n-seitigen polygonalen Wilsonschleifen in der N=4 supersymmetrischen Yang-Mills (SYM) Theorie beschreibt. Im ersten Teil dieser Dissertation wird die Wilsonschleifenseite einer solchen möglichen Dualität in der N=6 superkonformen Chern-Simons (ABJM) Theorie untersucht. Das Hauptergebnis dieser Untersuchungen ist, dass der Erwartungswert der n-seitigen polygonalen Wilsonschleifen auf Einschleifenebene verschwindet, während er auf Zweischleifenebene in seiner funktionalen Form identisch zu der analogen Wilsonschleife in N=4 SYM auf Einschleifenniveau ist. Außerdem wird eine anomale konforme Wardidentität für Wilsonschleifen in Chern-Simons Theorie berechnet. Zudem werden die damit im Zusammenhang stehenden Entwicklungen für Amplituden und Korrelatoren in der ABJM Theorie diskutiert. Im zweiten Teil dieser Dissertation werden Dreipunktfunktionen von zwei geschützten Operatoren und einem Twist-Zwei Operator mit beleibigem Spin j in der N=4 SYM Theorie berechnet. Dafür werden die Indizes des Spin j Operators auf den Lichtkegel projiziert und der Korrelator wird in einem Grenzfall untersucht in dem der Impuls der bei dem Spin j Operator einfließt verschwindet. Dieser Grenzfall vereinfacht die perturbative Berechnung erheblich, da alle Dreipunktdiagramme effektiv auf Zweipunktdiagramme reduziert werden und die Abhängigkeit der Mischungsmatrix auf Einschleifenebene herausfällt. Das Ergebnis stimmt mit der Analyse der Operatorproduktentwicklung von Vierpunktfunktionen geschützter Operatoren von Dolan und Osborn aus dem Jahre 2004 überein.
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investivated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop / amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N =4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

We study the target space duality of classical two dimensional sigma models. The models with dilaton and tachyon field are analyzed. As a motivating example the historical electric-magnetic duality is presented. We review the construction of the duality transformation and the integrability conditions for the nonlinear sigma models with target spaces described by general metrics and antisymmetric two-forms. We generalize the formalism for the models whose actions contain the dilaton and tachyon field. For the dilaton field case it is required that the duality is a property solely of the target manifolds, independent of the world-sheet geometry. For both cases the duality transformation is established and the integrability conditions are calculated. The set of restrictions on geometrical data describing the models is obtained, the previously calculated condition on connections on target spaces is maintained in both cases.

One of the most interesting problems in string theory is to understand how the background space-time on which the string propagates arises in a self-consistent way. For open strings, there are two main approaches to this problem, boundary string field theory (BSFT) and cubic string field theory (CSFT). In the first part of this Thesis we deal with the construction of the spacetime tachyon effective action in BSFT. Renormalization fixed points are solutions of classical equations of motion and should be viewed as solutions of classical string field theory. We have constructed the Witten-Shatashvili (WS) space-time action S and shown that some solitonic solutions are lower dimensional D-branes for which the finite value of S provides a quite accurate prediction of the D-brane tension. We have derived the explicit relation between the CSFT and WS action as a field redefinition which is nonsingular on-shell only when the normalization factor in the WS action coincides with the tension of the D25-brane, in agreement with the conjectures involving tachyon condensation. We have also found a time-dependent solution of CSFT whose evolution is driven by a diffusion equation that makes the equations of motion local with respect to the time variable. The analysis here proposed has attracted a good deal of attention for its potential cosmological applications. The profile can be expressed in terms of a series in powers of exponentials of the time coordinate, and gives evidence of a well-defined but wildly oscillatory behavior. The tachyon rolls well past the minimum of the potential, then turns around and begins to oscillate with ever increasing amplitude. Furthermore, we have derived an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude. From such a solution we computed the exact coefficient of the quartic effective action relevant for time-dependent solutions and we derived the exact coefficient of the quartic tachyon coupling. We studied the rolling tachyon solution expressed as a series of exponentials of the time coordinate both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level-truncated coefficients converge to those derived using the exact string amplitude and confirm the wild oscillatory behavior. In the second part of the Thesis we consider the extension of the gauge/gravity correspondence to systems with reduced and hence more realistic supersymmetry, which is one of the main steps towards a non-perturbative description of confining, QCD-like, gauge theories in terms of gravitational backgrounds. If string theory on AdS5xS5 is integrable, the theory on simple orbifolds of that space would also be expected to be integrable. We have computed the planar finite size corrections to the spectrum of the dilatation operator acting on states of a certain limit of conformal N = 2 quiver gauge field theory which is a ZM-orbifold of N = 4 SYM theory. We matched the result to the string dual, IIB superstrings on a pp-wave background with a periodically identified null coordinate. Up to two loops, we have shown that the computations done by using an effective Hamiltonian technique and a twisted Bethe Ansatz agree with each other and also agree with a computation of the analogous quantity in string theory. Our results are consistent with integrability of the N = 2 theory.

Orientador: Nathan Jacob Berkovits
Banca: Horatiu Stefan Nastase
Banca: Luis Raul Weber Abramo
Resumo: Esta tese consiste em uma revisão da estrutura da Teoria de Campo na Corda, focando nas propriedades clássicas do setor da corda aberta e suas possíveis aplicações para inflação. Portanto, seguiremos a prescrição do Witten e construiremos uma ação para a Teoria de Campo na Corda Aberta Bosônica. Então, percebendo que a teoria tem uma modo taquiônico e motivado pelo cenário de inflação, calcularemos e consideraremos o potencial taquiônico em alguma ordem de aproximação. Como aplicação, tomaremos o campo taquiônico como um candidato possível para o inflaton. A fim de trabalhar com esta proposta, revisaremos primeiramente a teoria inflacionária e estudaremos sua abordagem moderna, considerando apenas suas implicações a nível clássico utilizando a aproximação slow-roll. Finalmente, analisaremos o potencial taquiônico como sendo o potencial do inflaton e exploramos suas consequências. Como suporte, há quatro apêndices contendo alguns aspectos de Teoria de Cordas, Relatividade Geral, Cosmologia e alguns cálculos relevantes que foram omitidos ao longo da tese
Abstract: This thesis consists in a review of the String Field Theory framework, focusing in the classical properties of the open sector and its possible applications for inflation. Therefore, we intend to follow the Witten's prescription and build an action for the Open Bosonic String Field Theory. Then, recognizing that the theory has a tachyonic mode and motivated by the inflationary scenario, we calculate and consider the tachyonic potential in some order of approximation. As an application, we consider the tachyon field as a possible candidate for the inflaton. In order to work with this proposal, we first review the inflationary theory and study its modern approach, considering only its classical implications using the slow-roll approximation. Finally, we analyze the tachyonic potential as being the inflaton potential and explore its consequences. As a support, there are four appendices containing some aspects of String Theory, General Relativity, Cosmology and some relevant calculations that were omitted throughout the thesis
Mestre

The recent discovery of a new maximally supersymmetric background for the type IIB superstring theory has revived the interest in light cone string field theory. This background is a plane wave background with the additional support of a non- trivial self dual Ramond-Ramond 5-form field strength. It can be quantised in the light cone gauge and hence it naturally fits into the framework of light cone string field theory. In this thesis we re-examine the causality and locality properties of string theory in the flat background and compare it with the recent results for string theory in this plane wave background. We formulate the causality requirement in terms of the commutativity of the string field, as it is usually done in point particle field theory. We find that the string light cone in the plane wave background shares similar properties with the string light cone in the flat background. Even more interesting is that, unlike the flat background theory, string interactions in the plane wave background do not modify the causal structure of the theory. This has interesting consequences for the choice of the 3-string vertex in the plane wave background, a topic that is still an active subject of research.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
Includes bibliographical references (p. 133-144).
In this thesis we show how to calculate off-shell low energy effective actions and how to study the dynamics of the tachyon from string field theory. We discuss how to obtain an effective action for the massless field and we explain how to relate it to well known results. We then study the tachyon dynamics both in cubic and in boundary string field theory.
by Erasmo Coletti.
Ph.D.

The main topic of this doctoral thesis is D-branes in string theory, expressed in the language of conformal field theory. The purpose of string theory is to describe the elementary particles and the fundamental interactions of nature, including gravitation as a quantum theory. String theory has not yet reached the status to make falsifiable predictions, thus it is not certain that string theory has any direct relevance to physics. On the other hand, string theory related research has led to progress in mathematics.

We begin with a short introduction to conformal field theory and some of its applications to string theory. We also introduce vertex algebras and discuss their relevance to conformal field theory. Some classes of conformal field theories are introduced, and we discuss the relevant vertex algebras, as well as their interpretation in terms of string theory.

In string theory, a D-brane specifies where the endpoint of the string lives. Many aspects of string theory can be described in terms of a conformal field theory, which is a field theory that lives on a two-dimensional space. The conformal field theory counterpart of a D-brane is a boundary state, which in some cases has a natural interpretation as constraining the string end point. The main focus of this thesis is on the interpretation of boundary states in terms of D-branes in curved target spaces.

Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically unifies the spacetime metric and the gauge fields (and their local symmetries) in a generalized geometry. Solutions to these extended field theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the fivebrane in ordinary spacetime. In this thesis double field theory and exceptional field theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing singularities at the core of solutions and localizing them in winding space. The relation of exceptional field theory to F-theory is also covered providing an action for the latter and incorporating the duality between M-theory and F-theory.

The field equations of the vacuum Quadratic Poincare Gauge Field Theory are expressed in the spin coefficient formalism of Newman and Penrose. These equations are differential identities involving the curvature and torsion, and in this NewmanPenrose type approach must be combined with the generalized Newman-Penrose identities given in chapter 4. The use of this Newman-Penrose type formalism is demonstrated in the derivation of several new classes of exact solutions which would have been impossible to obtain by the various methods being used at this moment in time. This therefore demonstrates the power of the spin coefficient formalism developed in chapter 6. A brief look at SO(3) symmetric space-times, in the context of the vacuum Quadratic Poincare Gauge Field Theory, is taken in chapter 11. As a final consideration, a deeper look at the vacuum Quadratic Poincare Gauge Field Theory itself is taken, in order to see whether or not it is a reasonable Theory of Gravitation.

The purpose of this thesis is to study a symmetry of string theory known as T-duality. We focus on a particular example establishing the equivalence between a quantized string moving in a circular space of radius R and a dual string moving in a similar space of radius 1/R . We will show that this duality implies that the momentum of the string in one picture becomes the number of times the string is wound around the circle in the dual picture. We present two proofs of T-duality. The first reflects the standard interpretation of T-duality as an isomorphism of quantum theories. The second approach is based on Hull's Double Field Theory.

Dans cette thèse, nous présentons des avancements récents en Théorie des Champs Doubles (TCD) et Théories des Champs Exceptionnels (TCE). Ces théories ont la particularité d’être des reformulations de supergravité dans lesquelles les symétries de dualité sont explicites avant toute réduction dimensionnelle. Ces reformulations se basent sur la définition d’un espace-temps étendu qui géométrise le groupe de T-dualité en TCD et les groupes exceptionnels de U-dualité en TCE. Tous les champs de cet espace sont soumis à une contrainte de section qui restreint leur dépendance en coordonnées. Il existe plusieurs solutions à la contrainte de section, qui correspondent donc à des théories différentes. Dans ce sens, le formalisme des théories des champs étendues amène à une unification de ces théories. De plus, grâce à un outil spécifique aux théories des champs étendues, l’ansatz de Scherk-Schwarz généralisé, il est possible de réécrire les ansatz compliqué de type Kaluza-Klein en supergravité sous une forme élégante et compacte: un produit matriciel en dimensions supérieures. Ici, nous présentons plusieurs exemples de l’efficacité de l’ansatz de Scherk-Schwarz généralisé. En particulier, nous prouvons deux conjectures concernant les troncations cohérentes: la réduction dite “de Pauli” de la corde bosonique ainsi que la supergravité de type IIB sur AdS5 x S5. La dernière application de cet ansatz concerne la théorie de type IIB généralisée, apparue récemment dans l’étude des système intégrables, et son plongement dans la TCE E6(6). Enfin, nous présentons la complétion supersymétrique de la TCE E8(8) bosonique
In this thesis, recent developments in Double Field Theory (DFT) and Exceptional Field Theory (EFT) are presented. They are reformulation of supergravity in which duality symmetries are made manifest before dimensional reduction. This is achieved through the definition of an extended spacetime that “geometrises” the T-duality group O(d,d) in DFT and exceptional U-duality groups in EFT. All functions on this extended space are subject to a covariant `section constraint', whose solutions then restrict the coordinates dependency of the fields. There exist different solutions to the section constraint that correspond to different theories. In this sense, different theories are unified within the formalism of extended field theories. Moreover, extended field theories possess a powerful tool to study compactifications: the generalised Scherk-Schwarz ansatz.Here, we present several examples of the effectiveness of the generalised Scherk-Schwarz ansatz. In particular, we proved two conjectures regarding consistent truncations: the so-called Pauli reduction of the bosonic string on group manifolds and type IIB supergravity on AdS5 x S5. Another application is presented on the embedding of generalised type IIB within the E6(6) EFT, which recently appeared in the study of integrable systems.Finally, we present the supersymmetric completion of the bosonic E8(8) EFT

Recently, it has become increasingly clear that boundaries play a significant role in the understanding of the non-perturbative phase of the dynamics of strings. In this thesis we propose to study the effects of boundaries in non-critical string theory. We thus analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov's non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville field imply that the metric is discontinuous as the boundary is approached. We consider the semi-classical limit and argue how it singles out the free boundary conditions for the Liouville held. We define the open string susceptibility, the anomalous gravitational scaling dimensions and a new Yang-Mills Feynman mass critical exponent. Finally, we consider an application to the theory of non-critical dual membranes. We show that the strength of the leading stringy non-perturbative effects is of the order e(^-o(1/βst)), a result that mimics those found in critical string theory and in matrix models. We show how this restricts the space of consistent theories. We also identify non-critical one dimensional D-instantons as dynamical objects which exchange closed string states and calculate the order of their size. The extension to the minimal c ≤ 1 boundary conformal models is also briefly discussed.

In this work we review the basic principles of the theory of the relativistic bosonic string through the study of the action functionals of Nambu-Goto and Polyakov and the techniques required for their canonical, light-cone, and path-integral quantisation. For this purpose, we briefly review the main properties of the gauge symmetries and conformal field theory involved in the techniques studied.
Neste trabalho fazemos uma revisão dos princípios básicos da teoria da corda bosônica relativística através do estudo dos funcionais ação de Nambu-Goto e de Polyakov e das técnicas necessárias para sua quantização canônica, no cone de luz e usando integrais de trajetória. Para tanto apresentamos uma pequena revisão das principais propriedades das simetrias de calibre a da teoria de campos conforme envolvidas nas técnicas estudadas.

Some of the most interesting phenomena that arise from the developments of the modern physics are surely vacuum fluctuations. They appear in different branches of physics, such as Quantum Field Theory, Cosmology, Condensed Matter Physics, Atomic and Molecular Physics, and also in Mathematical Physics. One of the most important of these vacuum fluctuations, sometimes called "zero-point energy", as well as one of the easiest quantum effect to detect, is the so-called Casimir effect. The purposes of this thesis are: - To propose a simple retarded approach for dynamical Casimir effect, thus a description of this vacuum effect when we have moving boundaries. - To describe the behaviour of the force acting on a boundary, due to its self-interaction with the vacuum.