Добірка наукової літератури з теми "Gauge-Gravity dualities"

The AdS/CFT correspondence and its generalization to gauge/gravity dualities provide a very useful approach into solving strongly coupled systems. We put this at work for the strongly coupled sector of Composite Higgs models. We work out relations between masses of proposed states in Composite Higgs. As a cross check we compare these results to existing lattice calculations for which we find good agreement.

Dynamical electroweak symmetry breaking is an appealing, strongly coupled alternative to the weakly coupled models based on an elementary scalar field developing a vacuum expectation value. In Sections 2 and 3 of this set of lectures, I summarize the arguments, based on low-energy phenomenology, supporting walking technicolor as a realistic realization of this idea. This pedagogical introduction to walking technicolor, and more generally to the physics of extensions of the standard model, makes extensive use of effective field theory arguments, symmetries, and counting rules. The strongly coupled nature of the underlying interactions, and the peculiar quasiconformal behavior of the theory, requires to use nonperturbative methods in order to address many fundamental questions within this framework. The recent development of gauge/gravity dualities provides an ideal set of such nonperturbative instruments. Sections 4 and 5 illustrate the potential of these techniques with two technical examples, one within the bottom-up phenomenological approach to holography in five dimensions, the other within a more systematic top-down construction derived from ten-dimensional type-IIB supergravity.

We construct for the first time Drukker-Trancanelli (DT) type fermionic Bogomolǹyi-Prasad-Sommerfield (BPS) Wilson loops in four-dimensional \mathcal{N}=2𝒩=2 superconformal SU(N)\times SU(N)SU(N)×SU(N) quiver theory and \mathcal{N}=4𝒩=4 super Yang-Mills theory. The connections of these fermionic BPS Wilson loops have a supermatrix structure. We construct timelike BPS Wilson lines in Minkowski spacetime and circular BPS Wilson loops in Euclidean space. These Wilson loops involve dimensionful parameters. For generic values of parameters, they preserve one real (complex) supercharge in Lorentzian (Euclidean) signature. Supersymmetry enhancement for Wilson loops happens when the parameters satisfy certain constraints. The nature of such loops is quite different from the Wilson loop operators involving fermions constructed previously in the literature on four-dimensional gauge theories. We hope that further investigations of such new Wilson loops will explore deep structures in both the gauge theories and gauge/gravity dualities.

The ( 4 , 0 ) supermultiplet in six dimensions contains a fourth-rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32 + 32 supersymmetries. Dimensional reduction on a circle gives the five dimensions N = 8 supergravity multiplet, with the fourth-rank tensor reducing to the graviton. If there is an interacting ( 4 , 0 ) theory, it should reduce to the full N = 8 supergravity theory and so would give a conformal theory of gravity that would reduce to conventional gravity with the usual two-derivative action at low energies. This paper revisits the conjecture that a non-lagrangian interacting ( 4 , 0 ) superconformal theory arises from a strong coupling limit of five-dimensional supergravity (suitably embedded in M -theory) describing M -theory at energies beyond the Planck scale. A key test for this is identified: M -theory toroidally compactified to five dimensions should have certain BPS states carrying a singlet central charge. These 1/2 BPS states are not related to any of the standard BPS states by dualities and do not correspond to non-singular soliton solutions—they appear to correspond to singular solutions related to gravitational instantons. Such states are needed to provide the Kaluza–Klein modes for the compactified six-dimensional theory. If there are no such states, then the conjecture is false, while the presence of such states would be strong indication that the conjecture could be true.

This thesis consists in a self-contained study of gauge/gravity dualities in the line of the Klebanov-Witten model. Here we explore first the known Maldacena duality that relates N=4 SYM theory in four dimensions to type IIB supergravity on AdS_5×S^5 in reasonable detail, after some necessary preliminaries on supersymmetric gauge theories, where we display in detail the supersymmetry algebra and representations for N 1 supersymmetry. There we also construct the so-called superfields that will be helpful to write invariant lagrangians for gauge theoriesmreadily, and then useful to construct the gauge theory side of the Klebanov-Witten model. In the original AdS/CFT correspondence and its phenomenologically interesting extensions, Dp-branes as solutions of supergravity and nonperturbative objects in string theory where gauge theory lives are crucial. So, to preserve the self-contained nature of this work, we include a brief review of superstring theory addressed to understand the need to include this higher-dimensional objects by T-duality and, at low-energy limit of the string theory, as solutions of the Einstein equations. The first climax of this work occurs when we use all we learned to establish the Maldacena conjecture, N=4 SU(Nc) SYM theory we study in the supersymmetry chapter, living on the four-dimensional worldvolume of a stack of Nc D3-branes in a flat-space, corresponds exactly to type IIB supergravity on AdS_5×S^5 .In order to prove it, we match symmetries and operators with states in both sides. But actually this corresponds to the weak form of the correspondence, because it is not possible to handle neither string theory or gauge theory at strong coupling. The focus and main motive to have to learn the first hundred of pages here will be to extend the dual gauge theory we studied in AdS/CFT towards more realistic gauge theories as duals of some supergravity theory. The Klebanov-Witten model, consists in replacing the five-sphere in the gravity background of type IIB for a more interesting Einstein manifold X5 , a coset space called T^1,1 .The resulting dual gauge theory is expected to be less supersymmetric, and it is indeed N = 1 superconformal field theory with matter content in the bifundamental representation of the gauge group SU(N)×SU(N), and a quartic superpotential that exhibits SU(2)×SU(2)×U(1) global symmetry, which is precisely the symmetry of the coset space in the gravity side. This is not the end of the story, the Klebanov-Witten model extended the Maldacena correspondence and found as a dual gauge theory a less supersymmetric but still conformal theory. Breaking of the conformal theory, proposed by Klebanov, Nekrasov and Tseytlin, is achieved by introducing fractional M D3-branes in addition to the N regular D3-branes. The resulting theory is an SU(N+M)×SU(N) gauge theory with N = 1 supersymmetry, no longer conformal and then a little more interesting as a part of the crusade to find a QCD-like theory. This is still not the end, the last model suffers from a singularity in the deep IR, rendering the gravitational description invalid in that regime. It was conjectured that the strong dynamics of the gauge theory should somehow resolve this problem. Klebanov, again, and Strassler showed that this conjecture was correct, and argue that the RG flow is in fact an infinite series of Seiberg duality transformations- a cascade - in which the number of colors repeatedly drops from N NM , so the gaugegroup changes from SU(N+M)×SU(N) to SU(NM) ×SU(N). This process can be repeated until the IR limit where the gauge group simply becomes SU(M). So, at the end we get a N=1 SU(M) gauge theory, a QCD-like theory. We say that the standard model itself may lie at the base of a duality cascade.
Essa tese consiste num estudo autocontido das dualidades calibre/gravidade na linha do modelo do Klebanov-Witten. Aqui nos exploramos primeiro de um jeito razoavelmente detalhado,a conhecida dualidade do Maldacena que relaciona a teoria N=4 SYM em quatro dimensões com as supercordas tipo IIB no espaço AdS_5×S^5, depois de alguns preliminares necessários sobre teorias supersimétricas de calibre, onde nós mostramos em detalhe à algebra supersimétrica e as representações para N 1 supersimetria. Nós também construímos os conhecidos supercampos que são úteis para escrever lagrangianas invariantes para teorias de calibre facilmente, e então serão úteis para construir a teoría de calibre do modelo de Klebanov-Witten. Na correspondência AdS/CFT original e as suas extensões fenomenologicamente interessantes, as Dp-branas, como soluções de supergravidade e objetos não perturbativos na teoria de cordas onde as teorias de calibre moram, são essenciais. Assim ,a fim de preservar a natureza autocontida desse trabalho, nós incluímos uma breve revisão sobre teoria de supercordas dirigida a entender a necessidade de incluir esses objetos extra-dimensionais usando dualidade-T e, no limite de baixa-energia da teoria de cordas, como soluções das equações de Einstein. O primeiro clímax desse trabalho ocorre quando nós usamos tudo o que aprendemos para estabelecer a conjectura do Maldacena, a teoria de calibre N=4 SYM que nós estudamos no capítulo de supersimetria, morando no volume de mundo quadridimensional de uma pilha de Nc D3-branas (sim, o subscrito c significa cor!) em espaço plano, corresponde exatamente à teoria de supergravidade tipo IIB no espaço AdS_5×S^5 . A fim de testar ela, nós identificamos simetrias e operadores com estados em ambos lados da dualidade. Mas na verdade isto corresponde à forma fraca da correspondência, porque não é possível lidar nem com a teoria de cordas nem com a teoria de calibre no limite de acoplamento forte. O foco e motivo principal de porque nós temos que aprender as primeiras cem páginas aqui, será estender a teoria de calibre dual que estudamos em AdS/CFT, para teorias de calibre mais realisticas como duais de alguma teoria de supergravidade. O modelo do Klebanov-Witten, consiste em substituir a esfera de cinco dimensões no fundo de supergravidade da teoria de supercordas tipo IIB por um espaço que é mais interessante X5, um espaço coset chamado T^1,1. Nós esperamos que a teoria de calibre dual que resulta é menos supersimetrica, e na verdade é N =1 superconforme com um conteúdo de matéria na representação bifundamental do grupo de calibre SU(N)×SU(N), e um superpotencial quártico que tem simetria global SU(2)×SU(2)×U(1), que é precisamente a simetria do espaço coset no lado da gravidade. Mas isso não é tudo, o modelo do Klebanov-Witten estendeu a correspondência do Maldacena e encontrou como teoria dual uma teoria menos supersimetrica mas ainda conforme. A quebra da simetria conforme, proposta pelo Klebanov, Nekrasov e Tseytlin, é obtida introduzindo M D3-branas fracionais além das N D3-branas regulares. A teoria resultante é uma teoria de calibre SU(N+M)×SU(N) com N = 1 supersimetria, não mais conforme e então um pouco mais interessante como parte da nossa cruzada para encontrar uma teoria tipo-QCD. Isso ainda não é o final, o modelo anterior sofre de uma singularidade no IR profundo, tornando inválido a descrição gravitacional. Foi conjeturado então que a dinâmica do acoplamento forte na teoria de gauge deveria de algum jeito resolver esse problema. Klebanov, de novo, e Strassler mostraram que essa conjetura foi correta, e argumentaram que o fluxo do GR é de fato uma serie infinita de transformações de dualidade de Seiberg - uma cascata - onde o numero de cores cai repetidamente de NNM, e o grupo de calibre muda de SU(N+M)×SU(N) a SU(NM)×SU(N). O processo pode ser repetido até o limite IV onde o grupo de calibre simplesmente torna-se SU(M). Então, no final nós obtemos uma N = 1 teoria de calibre SU (M ), ou seja uma teoria tipo-QCD. Então, nós dissemos que o modelo padrão mesmo pode se situar na base da cascata de dualidade.

We examine the use of branes as probes of supergravity geometries which arise in the study of gauge theory/gravity dualities. We investigate the moduh spaces of supersymmetric gauge theories through moduh spaces of brane probes in the dual gravity theories. Preferred coordinate systems emerge in which the supergravity geometries can readily be compared to the gauge theory and various gauge theory quantities such as anomalous scaling dimensions can be read off. We also consider the physics of certain expanded brane configurations, called giant gravitons. We identify supergravity solutions which represent coherent states of these objects. We find a degeneracy between giant graviton probes and massless particles in a broad class of supergravity backgrounds and uncover a close relationship with charged particle states in lower dimensions.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.
Includes bibliographical references (p. 179-194).
At present, there are no non-perturbative analytic methods available for investigating gauge theories at large couplings. Consequently, it is desirable to explore more avenues to gain qualitative and quantitative insights. The gauge/gravity (AdS/CFT) correspondences provides a unique opportunity to study gauge theories both at finite and zero temperatures in the strong coupling regime, potentially leading to insights into QCD. In this regime, where both the 't Hooft coupling and the number of colors is large, the dynamics of the gauge theory is described by super gravity solutions, which describe the low-energy limit of systems of D-branes. In this dissertation, I use the AdS/CFT correspondence to study the dispersion relations of mesons in a particular hot, strongly coupled, supersymmetric gauge theory plasma. This plasma arises by placing a probe D7-brane in the near-horizon geometry of non-extremal D3-branes. I find the large momentum dispersion relations of scalar mesons and extract from them their limiting velocity vo, which depends only on the ratio of the temperature to the quark mass. I use vo to find that the temperature above which no meson bound states with velocity v exist is Tdiss(V) - (1 - v2)1/4Tdiss(v = 0). This agrees with results inferred indirectly via analysis of the screening length between a static quark and anti quark in a moving plasma. Although these calculations are not done in QCD, I argue that the qualitative features of my results may apply to bottomonium and charmonium mesons propagating in the strongly coupled QCD plasma. To aid further investigations of the effect of fundamental matter on hot gauge theory plasmas I find the non-extremal, localized D2/D6-brane solution in its linear limit. Pursuing a different direction, I consider a stack of N D3-branes and M D5-branes wrapped at the apex of a cone over Sasaki- Einstein spaces yp,q. Replacing the D-branes by their fluxes, I construct asymptotic solutions for all p and q in the form of warped products of the cone and R" 3. These theories are not conformal, and the solutions describe cascading renormalization group flows.
by Qudsia Jabeen Ejaz.
Ph.D.

Motivated by the AdS/CFT correspondence, new supersymmetric solutions to Type IIB and Type IIA supergravity are presented. These solutions contain $AdS_5$ or $AdS_4$ factors and are generated using T-duality symmetries of supergravity. The technique used to generate these solutions consists of performing a series of non-Abelian and Abelian T-dualities, sometimes with coordinate shifts in-between, to Freund-Rubin type seed backgrounds. An added bonus of the gauge fixing procedure inherent in non-Abelian T-Duality is the freedom to generate backgrounds with extra free parameters, some examples of which are presented. Aspects of the dual field theories of these new solutions are analyzed using holography techniques. The supersymmetry of these new backgrounds is also discussed. In addition to supergravity backgrounds with AdS, the study of generalized Calabi-Yau manifolds in the context of flux compactifications is briefly reviewed. The particular case of the resolved cone over $Y^{p,q}$ and its admission of generalized SU(3) structure solutions is examined. Contrary to geometries with $AdS$ factors, whose field theory duals are conformal field theories, these types of geometries can be phenomenologically interesting to study, as their gauge theory duals are minimally supersymmetric and confining, thus they could someday help aid our understanding of strongly-coupled QCD (Quantum Chromodynamics).

Cette thèse porte sur l'étude de système quantique intégrable spécifique ``chaînes de spin'' présentant différentes symétries. Ces chaînes de spin sont considérées comme des modèles jouets de certaines théories bidimensionnelles des champs lorsque la taille de ces modèles est finie. En particulier, certaines relations fonctionnelles dans ces chaînes de spin ont été généralisées aux théories des champs en utilisant un nombre fini d'équations pour trouver leur spectre.Nous commençons cette thèse en décrivant la chaîne de spins rationnelle bien étudiée avec symétrie GL(n) en utilisant l'opérateur de ``codérivée'' pour construire un « opérateur Q » polynomial qui nous permet de diagonaliser l'hamiltonien. Nous montrons l'équivalence avec une autre construction s'appuyant sur des représentations explicites en termes d’oscillateurs harmoniques.Nous étudions ensuite une chaîne de spins moins connue présentant une symétrie SO(2r). Nous construisons le ``Q-opérateur'' pour les représentations connues. Nous essayons ensuite plusieurs méthodes pour construire lesdits opérateurs pour des représentations générales. Ces tentatives montrent clairement que, d’une part, elles suggèrent fortement que la codérivative n’est pas suffisante pour décrire des représentations générales dans l’espace auxiliaire. Nous espérons en revanche qu’ils aideront à trouver quels outils supplémentaires pourraient nous permettre de les décrire
This thesis is concerned with the study of specific integrable quantum system ``spin chains'' with different symmetries. These spin chains are considered toy models of some two-dimensional field theories when the size of these models is finite. In particular, some functional relations in these spin chains were generalized to field theories using a finite number of equations to find their spectrum.We start this thesis by describing the well-studied rational spin chain with GL(n) symmetry using the Coderivative operator to build a polynomial ``Q-operator'' that allows us to diagonalize the Hamiltonian. We show the equivalence with another construction relying on representations that are explicit in terms of harmonic oscillators.We then study a lesser-known spin chain with SO(2r) symmetry. We build the ``Q-operator'' for the known representations. Then we attempt several methods to build said operators for general representations. These attempts clearly show that, on the one hand, the attempts strongly suggest the Coderivative is not sufficient to describe general representations in auxiliary space. On the other hand, we hope they will help to find what additional tools may allow us to describe them

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014.
In this dissertation we compute the anomalous dimensions for a class of operators, belonging to the SU(3) sector of the theory, that have a bare dimension of order N. For these operators the large N limit and the planar limit are distinct and summing only the planar diagrams will not capture the large N dynamics. Although the spectrum of anomalous dimensions has been computed for this class of operators, previous studies have neglected certain terms which were argued to be small. After dropping these terms diagonalizing the dilatation operator reduces to diagonalizing a set of decoupled oscillators. In this dissertation we explicitely compute the terms which were neglected previously and show that diagonalizing the dilatation operator still reduces to diagonalizing a set of decoupled oscillators.

The thesis covers two topics in string theory and quantum field theory. First, we realize metastable vacua in various supersymmetric gauge theories. Specifically, we consider the Coulomb branch of any N = 2 supersymmetric gauge theory, and perturb it by a superpotential and engineer a metastable vacuum at a point. We also study its relation to Kahler normal coordinates and Fayet-Iliopoulos terms. Having studied the metastable construction, we apply this to general gauge mediation. We show how to compute the current correlators when the hidden sector is strongly coupled in specific examples.

Next, we consider gauge/gravity dualities. We apply dualities to the investigation of various strongly coupled field theories. In one example, we construct M-theory supergravity solutions with the nonrelativistic Schroedinger symmetry starting from the warped AdS_5 metric with N = 1 supersymmetry. We impose that the lightlike direction is compact by making it a nontrivial U(1) bundle over the compact space. In another example, we show that, in a gravity theory with a Chern-Simons coupling, the Reissner-Nordstrom black hole in anti-de Sitter space is unstable depending on the value of the Chern-Simons coupling. The analysis suggests that the final configuration is likely to be a spatially modulated phase.