Academic literature on the topic 'Vacuum String Field Theory'

String theory has emerged as the leading candidate for a unified field theory of all known forces. However, it is impossible to trust the various phenomenological predictions of superstring theory based on classical solutions alone. It appears that the crucial problem of the theory, breaking ten dimensional space-time down to four dimensions, must be solved nonperturbatively before we can extract reliable predictions. String field theory may be the only formalism in which we can resolve this decisive question. Only a rigorous calculation of the true vacuum of the theory will determine which of the many classical solutions the theory actually predicts. In this review article, we summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. We also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group we call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU (N). Thus, the geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge 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.

Abstract This work depicts an experimental method for the validation of an Atomistic Field Theory (AFT) model for contact electrification of dielectrics. The AFT model is used to simulate the effects of Triboelectric Nanogenerators (TENGs) for energy harvesting. Recently, the AFT model has shown that contact electrification can be described by the induced surface dipoles when two dissimilar materials are brought into close contact assuming that the crystal lattices are free of defects, no residual strain in the materials is present and that the experiment is performed in vacuum. These simulations have been used to predict the induced contact potential between MgO and BaTiO3. To validate the AFT model, a set of quasi-static experiments will be conducted to test two different operating modes of TENGs, which can be mirrored in the simulations. The first experiment is a micro-scale pull-in/pull-off test in which a pad of single crystal Si (SCSi) will be brought into and out of contact with a dielectric substrate (thermally grown SiO2). The second experiment will mimic the TENG during sliding operation. A SCSi microcantilever will be brought into contact with the dielectric surface and displaced in sliding mode. These experiments will be conducted using a custom, reusable MEMS load cell and an electrometer to monitor the interaction forces and induced charge on the surfaces. To obtain the required displacement resolution of the load cell, a high-speed Michelson interferometer will be used. This allows for higher load cell stiffness to accommodate for surface adhesion effects. The load cell will be calibrated using the well-known technique of hanging masses from the load cell. The relative distance between the interacting surfaces in both experiments will be controlled by a piezo stage with 1 nm resolution. Results from these experiments are to be compared to the AFT model results.