The discovery of integrability on both sides of the duality between planar N=4 super Yang-Mills theory and free type IIB string theory in AdS5 × S5 has lead to great progress in our understanding of the AdS/CFT correspondence. Similar integrable structures also appear in the more recent three-dimensional superconformal N=6 Chern-Simons-matter theory constructed by Aharony, Bergman, Jafferis and Maldacena (ABJM), as well as in its gravity dual, type IIA string theory on AdS4 × CP3. However, new interesting complications arise in the AdS4/CFT3 duality. In the conjectured all-loop Bethe equations by Gromov and Vieira the dispersion relation of the magnons has a non-trivial coupling dependence which is parametrized by a function that is only known to the leading order at weak and strong coupling. In the first part of this thesis I discuss our calculations of the next-to-leading correction to this function at weak coupling. We compute this function from four-loop Feynman diagrams in the SU(2) × SU(2) sector of the ABJM model. As a consistency check we have performed the calculation both in a component formalism and using superspace techniques. At strong coupling the fundamental excitations of the integrable model are the giant magnons. The topic of the second part of this thesis is the spectrum of these giant magnons in CP3. Furthermore, I discuss our analyses of the finite-size corrections beyond the asymptotic Bethe ansatz. At weak coupling we have computed the leading four-loop wrapping diagrams in the ABJM model. At the strong coupling side of the duality I discuss our results for the exponentially suppressed finite-size corrections to the energy of giant magnons.

This thesis investigates applications of the gauge/gravity duality to strongly coupled quantum field theories. After a review of the duality and of correlators and transport in quantum systems, we present our results on second-order non-conformal hydrodynamics. We derive new Kubo formulae for five second-order transport coefficients in non-conformal relativistic fluids. We then apply these Kubo formulae to a class of non-conformal holographic fluids at infinite coupling. We find strong evidence that the Haack-Yarom identity, known to relate second-order coefficients in conformal holographic fluids at infinite coupling, continues to hold in holographic fluids without conformal symmetry: Within our class of models, we prove that it still holds when leading non-conformal corrections are taken into account, and we show numerically that it is also obeyed beyond leading order. This provides further evidence that the identity may be a universal feature of strongly coupled fluids. Next, we present our results on magnetic spin impurities in strongly correlated systems. We build a holographic two-impurity Kondo model, identifying the inter-impurity interaction as double-trace deformation. Our numerical results for the phase diagram suggest a quantum phase transition between a trivial phase with uncorrelated spins and no Kondo screening, and a non-trivial phase with anti-ferromagnetic correlations and simultaneous Kondo screening. Computing the spectrum in the single-impurity case, we observe Fano resonances, which at low temperatures we identify with the Kondo resonance.

The aim of the thesis is to study the AdS/CFT correspondence and the AdS2/SYK connection as a very special example of the duality. While the first part of the thesis contains a review of AdS/CFT correspondence in arbitrary dimensions, the later parts focus on an interesting and speculative connection between the gravitational physics in two dimensional nearly AdS2 spacetime and one dimensional SYK model. More specifically, the connection is realized in terms of certain features of the SYK model in strong coupling limit, which resembles those of nearly AdS2 Jackiw-Teitelboim theory.

In this thesis we study gauge/gravity duals in the 5d/6d AdS/CFT correspondence. We start with field theories defined on squashed five-spheres with SU(3) × U(1) symmetry. These five-sphere backgrounds are continuously connected to the round sphere. We find a one-parameter family of 3/4 BPS deformations and a two-parameter family of (generically) 1/4 BPS deformations. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplift to massive type IIA supergravity. We holographically renormalize the Romans theory, and use our general result to compute the renormalized on-shell actions for the solutions. The results agree perfectly with the large N limit of the dual gauge theory partition function, which we compute using large N matrix model techniques. In addition we compute BPS Wilson loops in these backgrounds, both in supergravity and in the large N matrix model, again finding precise agreement. We conjecture a general formula for the partition function on any five-sphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector. We then proceed to study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions to the squashed five-sphere background. We also analyse the classification of gravity duals with zero B-field.

Submitted by THIAGO ROCHA ARAUJO (taraujo@ift.unesp.br) on 2016-02-18T13:06:31Z No. of bitstreams: 1 thesis.pdf: 2041737 bytes, checksum: e20834514f664eb4d2cf9905a1e49015 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-02-19T19:04:25Z (GMT) No. of bitstreams: 1 araujo_tr_dr_ift.pdf: 2041737 bytes, checksum: e20834514f664eb4d2cf9905a1e49015 (MD5) / Made available in DSpace on 2016-02-19T19:04:25Z (GMT). No. of bitstreams: 1 araujo_tr_dr_ift.pdf: 2041737 bytes, checksum: e20834514f664eb4d2cf9905a1e49015 (MD5) Previous issue date: 2016-02-16 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Nessa tese estudamos propriedades de soluções de supergravidade tipo II obtidas através da dualidade T abeliana e não abeliana. Também determinamos, através da conjectura gauge/gravidade, aspectos da teoria de campos dual a essas soluções obtidas por dualidade T. Consideramos três tipos distintos de soluções: duais a teorias de campos que confinam, duais a teoria de campos conformes e duais a teoria de campos não-relativistas. Concluimos essa tese com uma análise dos laços de Wilson em soluções com simetria não relativista. / In this thesis we study properties of type II supergravity solutions generated by abelian and nonabelian T-duality. Also we determine, through the gauge/gravity conjecture, some aspects of the field theory dual to the supergravity solutions obtained by T-dualization. We consider three distinct types of backgrounds solutions, namely, backgrounds that are dual to confining field theories, backgrounds dual to conformal field theories and those dual to nonrelativistic field theories. We conclude this thesis with an analysis of Wilson loops on backgrounds with nonrelativistic symmetries. / CNPq: 140588/2012-4

The gauge/string duality, a.k.a. the holographic principle is a profound assertion that emerged from string theory. It relates strongly-coupled gauge theories to weakly coupled string theories living in a higher-dimensional curved geometry. Nevertheless, it is a conjecture, and only a few instances of its more concrete form, the AdS/CFT correspondence, are well-understood. The most well-studied example is the duality between N=4 SYM, which is a CFT, and type IIB string theory in AdS5xS5 background. Generalization to less symmetric cases is a must, and the next logical step is to add a mass scale to N=4 SYM, therefore breaking its conformal symmetry and leading to N=2* SYM, the theory we study in this thesis. It is supersymmetric enough to employ the powerful localization method that reduces its partition function to a matrix model. We will see that the mass scale causes non-trivial phase structures in its vacuum configuration, visible in the holographic regime. We will probe them using Wilson loops in different representations of the gauge group. On the other hand, the dual supergravity background was derived by Pilch-Warner, making N=2* theory an explicitly testable non-conformal holographic case, which is a rare example. We will prove that the duality works for the dual observables (string action, D-branes) we managed to compute, even at a quantum-level.

abstract: Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law of thermodynamics applied to local holographic screens. This is accomplished by essentially reversing the steps of Hawking's area theorem, leading to the Ricci convergence condition as an input, from which an application of Einstein's equations yields the NEC. Using the same argument, I show logarithmic quantum corrections to the Bekenstein-Hawking entropy formula do not alter the form of the Ricci convergence condition, but obscure its connection to the NEC. Then, by attributing thermodynamics to the stretched horizon of future lightcones -- a timelike hypersurface generated by a collection of radially accelerating observers with constant and uniform proper acceleration -- I derive Einstein's equations from the Clausius relation. Based on this derivation I uncover a local first law of gravity, connecting gravitational entropy to matter energy and work. I then provide an entanglement interpretation of stretched lightcone thermodynamics by extending the entanglement equilibrium proposal. Specifically I show that the condition of fixed volume can be understood as subtracting the irreversible contribution to the thermodynamic entropy. Using the AdS/CFT correspondence, I then provide a microscopic explanation of the 'thermodynamic volume' -- the conjugate variable to the pressure in extended black hole thermodynamics -- and reveal the super-entropicity of three-dimensional AdS black holes is due to the gravitational entropy overcounting the number of available dual CFT states. Finally, I conclude by providing a recent generlization of the extended first law of entanglement, and study its non-trivial 2+1- and 1+1-dimensional limits. This thesis is self-contained and pedagogical by including useful background content relevant to emergent gravity. / Dissertation/Thesis / Doctoral Dissertation Physics 2020

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21561号 / 理博第4468号 / 新制||理||1641(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 福間 將文, 教授 田中 貴浩, 准教授 國友 浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21567号 / 理博第4474号 / 新制||理||1642(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高柳 匡, 教授 青木 慎也, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The N= 4 Super Yang-Mills theory in four dimensions admits deformations and the exactly marginal deformations of its SU(3) R-symmetry sub-sector are known as Leigh-Strassler. Leigh-Strassler deformations break the N= 4 supersymmetry down to N= 1 while preserving conformal symmetry. With exactly marginal deformations only the F-terms are deformed thus Leigh-Strassler deformations only affect the superpotential in the Lagrangian. In this thesis we study the symmetry of the marginally deformed N= 4 SYM and demonstrate that its algebraic structure can be understood in terms of quasi-Hopf algebras. Quasi-Hopf algebras have a notion of twisting due to Drinfeld which makes them a natural mathematical language with which to treat deformations. Furthermore the deformation of the N= 4 SYM superpotential is automated by the definition of a suitable star product. / Thesis (PhD)--University of Pretoria, 2020. / NiTheP / Physics / PhD / Unrestricted