Academic literature on the topic 'Gauge/gravity duality, entanglement in holography'

We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with Uk(N) × U-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)=ℤk × SO(4)=ℤk isometry. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein (KK) holography to the LLM geometries. We focus on the chiral primary operator (CPO) with conformal dimension Δ = 1. The non-vanishing vacuum expectation value (vev) implies the breaking of conformal symmetry. In that case, we show that the variation of the holographic entanglement entropy (HEE) from it’s value in the CFT, is related to the non-vanishing one-point function due to the relevant deformation as well as the source field. Applying Ryu Takayanagi’s HEE conjecture to the 4-dimensional gravity solutions, which are obtained from the KK reduction of the 11-dimensional LLM solutions, we calculate the variation of the HEE. We show how the vev and the value of the source field determine the HEE.

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS2. We propose a generic dual theory of gravity in the AdS2 and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still “freezes” as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

We study a generalD-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.

PT quantum mechanics studies the physics of non-Hermitian Hamiltonians having an anti-linear involution denoted by PT as a symmetry. We extend the concept of PT non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. We identify how key properites such as the PT phase transition are implemented in the gauge-gravity duality. Then we move on to study time dependent systems (holographic quantum quenches) and discuss how Hermitian and non-Hermitian time evolution arise in PT quantum mechanics and how it is implemented in the gauge-gravity duality. A key feature is that the non-Hermitian time evolution violates the null energy condition (NEC) and speculate about possible applications.

In this work, we study the transport coefficients of strongly coupled condensed matter systems using gauge/gravity duality (holography). We consider examples from the real world and evaluate the conductivities from their gravity duals. Adopting the bottom-up approach of holography, we obtain the frequency response of the conductivity for (1+1)-dimensional systems. We also evaluate the DC conductivities for non-relativistic condensed matter systems with hyperscaling violating geometry.

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1 + 1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados–Teitelboim–Zanelli (BTZ) black hole, the Gibbons–Hawking–York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

We review some recent progress in studying the nuclear physics especially nucleon-nucleon (NN) force within the gauge-gravity duality, in context of noncritical string theory. Our main focus is on the holographic QCD model based on the AdS6background. We explain the noncritical holography model and obtain the vector-meson spectrum and pion decay constant. Also, we study the NN interaction in this frame and calculate the nucleonmeson coupling constants. A further topic covered is a toy model for calculating the light nuclei potential. In particular, we calculate the light nuclei binding energies and also excited energies of some available excited states. We compare our results with the results of other nuclear models and also with the experimental data. Moreover, we describe some other issues which are studied using the gauge-gravity duality.

The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand these bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1 + 1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multiscale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error–correcting codes and tensor networks. This work is expected to stimulate a more comprehensive study of tensor network models capturing bulk-boundary correspondences.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 73-77).
In this thesis, we present studies that elucidate the relationship between entanglement in strongly coupled gauge theories and the geometry of their gravity duals. In the first, we find that in a certain class of time-dependent states which have a gravity dual in which a black hole forms, the entanglement entropy of large regions grows linearly in time, following the growth of certain time-like slices in the interior of the black hole. In the second, we find a unified prescription in the gravity dual for calculating the action of the entanglement Hamiltonian associated to an arbitrary spatial region in a given holographic state. In particular, we find that the linearized perturbation of the metric caused by the entanglement Hamiltonian propagates from the bulk entangling surface.
by Sunok Josephine Suh.
Ph. D.

This thesis investigates a number of topics relating to flavour physics and entanglement within gauge/gravity duality, or ‘holography’, which is a framework for studying equivalences between certain gravitational and non-gravitational theories. The field arose from generalisations of the original AdS/CFT correspondence, which postulated the equivalence between the N = 4 super Yang-Mills gauge theory and type IIB superstring theory on AdS5 × S5. The duality is such that the gauge theory is strongly-coupled when the string theory reduces to a classical supergravity theory, and consequently provides a new method of computation for strongly coupled physics such as QCD and many condensed matter systems. In this thesis we study applications of gauge/gravity duality to flavour physics, and both applications and fundamental issues of entanglement within the holographic framework. We study a holographic model of graphene in a cavity and find a new controlled example of mass gap generation, and a new phase in which a graphene sheet condenses with its mirror image. We then study a bottom-up model known as Dynamic AdS/QCD, and reproduce soft wall behaviour needed to obtain the known Regge behaviour for meson masses, discussing some inherent limitations in the approach. The discussion then moves onto the entanglement of flavour in AdS/CFT, and we compute the entanglement entropy in detail for the massive D3/D7 system, and present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography. Finally, we study the issue of entanglement entropy in generic top-down models, and provide strong evidence that it can be computed via a generalisation of the Ryu-Takayanagi formula, using codimension two minimal surfaces which asymptotically wrap the compact part of the geometry.

The sequence of chapters can be divided into three blocks. - The first block contains the introductory chapters. In chapter 1 we illustrate the problem of the high-Tc superconductors making a parallelism between the Fermi Liquid theory, the BCS theory of superconductivity and the theory which is currently supposed to describe electron doped high-Tc superconductors at weak coupling. In chapter 2 we describe the aspects of the AdS/CFT correspondence that will be relevant throughout the reading of the thesis. - The second block coincides with chapter 3. In this chapter we define the concept of holographic superconductivity and we study phenomenological models of holographic superconductors. These are bottom-up models in the sense that they do not come from any particular string theory. This chapter has several important results, among them we mention, the classification of the holographic phase transitions and the characterization of the optical conductivity. - The third block contains the chapters from 4 to 7. The mainstream is the study of top-down models of holographic superconductors that naturally arise as smaller sectors of consistent truncations of type IIB supergravity. In chapter 4 we consider N = 8 supergravity and we describe the building blocks of N = 2 supergravity looking for such holographic superconductors. In this setup, the AdS/CFT dictionary is very well understood and we identify the analog of a Cooper pair state. In chapter 5, we discuss holographic superconductivity in the type IIB theory on AdS5 x S5 whereas in chapter 6, we consider the more general setting of type IIB theory compactified on Sasaki-Einstein manifolds. Among several examples, we will consider the interesting case of AdS5 x T1;1. In chapter 7, we study a four dimensional N = 2 supergravity which is related to M-theory, we find a novel family of holographic superconductor and we describe in detail the properties of gravitational background providing its interpretation in the dual field theory. We close the discussion about phenomenological models of holographic superconductivity and supergravity with conclusions and outlook. Finally, the thesis is equipped with two appendices in which we set up the the notation that will be adopted in the various chapters. Both these appendices are also thought as a quick and practical reminder of known results in the literature about field theory and supergravity.
En aquesta tesi es defineix el concepte de la superconductivitat hologràfica i s'estudien models fenomenològics dels superconductors hologràfics i models de superconductors hologàfics que deriven de la teoria de cordes. Els primers dos capítols són capítols introductoris. En el primer s'il.lustra el problema dels superconductors d'alta temperatura. En el segon es descriuen els aspectes de la correspondència que seran rellevants al llarg de la lectura de la tesi. En el capítol 3 estudiem els models fenomenològics i presentem diversos resultats importants, entre ells podem esmentar, la classificació de les transicions de fase en la teoria hologràfica i la caracterització de la conductivitat òptica. Després, la temàtica principal va canviar cap a l'estudi de models de superconductors hologràfics que deriven de la teoria de cordes i que s'obtenen a partir de truncaments consistents de la supergravetat de tipus IIB. En el capítol 4 considerem la supergravetat N = 8 en cinc dimensions i descrivim les característiques generals de la supergravetat N = 2. Utilitzem aquesta teoria per trobar models de superconductors hologràfics que venen de la teoria de cordes. En aquest cas, el diccionari de la correspondència AdS/CFT s'entén bé i ens permet identificar l'anàleg d'un parell de Cooper. En el capítol 5, es discuteix la superconductivitat hologràfica en la teoria de tipus IIB compactificat sobre AdS5 x S5, mentre que en el capítol 6, considerem el context més general de la teoria de tipus IIB compactificat sobre varietat de Sasaki-Einstein. Entre diversos exemples, considerem el cas interessant de AdS5 x T1;1. En el capítol 7, estudiem un model de supergravetat N = 2 en quatre dimensions que es relaciona amb la teoria M, ens trobem amb una nova família de superconductors hologràfics i descrivim en detall les propietats de l'espai gravitacional, tot seguit, proporcionem la seva interpretació en la teoria dual de camps. La tesi finalitza amb una discussió de caràcter general sobre els models fenomenològics de la superconductivitat hologràfica i la supergravetat.

Holographic dualities are now an established tool in the study of universal properties of strongly coupled field theories. Yet, theories without translational symmetry are still poorly understood in this context. In this dissertation, we investigate three new approaches to this challenging problem. The first part of the dissertation concerns a class of phenomenological holographic models in which momentum relaxation can be achieved without breaking translational symmetry in the dual geometry. In particular, we focus on an example in which the dual geometry is similar to anti-de Sitter (AdS) Brans-Dicke theory. We study the thermodynamic and transport properties of the model and show that for strong momentum relaxation and low temperatures the model has insulator-like behaviour. In the second part, we go beyond the effective description and consider holographic theories which explicitly break translational symmetry. From the perspective of gravity, these theories translate to geometries that vary explicitly in the boundary space-like coordinates. We refer to these geometries as 'inhomogeneous' and investigate two approaches to study them. The first is motivated by the question: "what happens to a homogeneous geometry when coupled with a field varying randomly in space?". Starting from an AdS geometry at zero or finite temperature, we show that a spatially varying random Maxwell potential drives the dual field theory to a non-trivial infra-red fixed point characterised by an emerging scale invariance. Thermodynamic and transport properties of this disordered ground state are also discussed. The second is motivated by the complementary question: "how does a random geometry affect a probe field?". In the weak disorder limit, we show that disorder induces an additional power-law decay in the dual correlation functions. For certain choices of geometry profile, this contribution becomes dominant in the infra-red, indicating the breaking of perturbation theory and the possible existence of a phase transition induced by disorder. The third and last part of this dissertation switches from the gravity to the field theoretical side of the duality. We discuss the Sachdev-Ye-Kitaev (SYK) model, a disordered many-body model with distinctive black hole-like properties. We provide analytical and numerical evidence that these holographic properties are robust against a natural one-body deformation for a finite range of parameters. Outside this interval, this system undergoes a chaotic-integrable transition.

In this thesis various holographic models are treated, which describe theories of fields where an internal symmetry is broken, either in relativistic contexts, or in case of violation of the Lorentz invariance.The first chapter opens with the revision of the notion of symmetry breaking in pure relativistic field theory. The case of spontaneous breaking and the Goldstone theorem are discussed, as well as the case of explicit breaking, where precise Ward identities between conserved current correlators and scalar operators loaded under such current are derived in a completely general way.We then consider two examples of non-relativistic field theories, which will be reproduced by holographic models: a model in which the invariance of boosts is broken by the presence of a chemical potential, and a model of Lifshitz's invariant theory. We show the non-relativistic realization of Ward's identities for the symmetry breaking.In the second chapter we briefly introduce the correspondence gravitation / gauge theory and we revise the central tool of this thesis, the holographic renormalization.In the third chapter, we show how to generate field theories with symmetry breaking by coupling a scalar field to a gauge field, and holographically deriving the Ward identities predicted by the field theory arguments, first in the Relativistic case. We also obtain an analytic expression for the scalar two-point function, where we know how to find the massless boson of Goldstone and the mass of linear mass in the explicit breaking parameter Of the Goldstone pseudo-boson, respectively in the purely spontaneous case and in the case of an explicit small break.We also consider the two-dimensional case on the edge, where we find that Coleman's theorem is eluded in the wide limit of $ N $, and Ward's identities are not affected.For non-relativistic cases, we first consider a non-abelian model in which the Lorentz invariance is broken: this situation makes it possible to observe so-called ~ B bosons which exhibit a quadratic dispersion relation and do not respect Not the law of a single Goldstone mode for each broken generator.Finally, we study in detail the holographic renormalization and the two-point functions for a conserved current and various scalar operators in a space-time of Lifshitz. We also find the Ward identities of symmetry breaking in their non-relativistic realization.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

The holographic principle has become an extraordinary tool in theoretical physics, most notably in the form of the Anti-deSitter Conformal Field Theory (AdS/CFT) correspondence, in which classical gravitational degrees of freedom in N-dimensions are related quantum field theory degrees of freedom in N − 1 dimensions in the limit of a large number of fields. Here we present an account of the AdS/CFT correspondence, also known as the gauge/gravity duality, from its origins in the large N 'tHooft expansion, up to Maldacena's proposal that type IIB string theory in the presences of D-branes at low energy is dual to an N = 4, d = 4, U(N) super Yang-Mills on AdS5 × S5 . We begin with an extensive review of (super)string theory including D-branes. We then present the general formulation of the AdS/CFT in the supergravity background of AdS5 × S5 , along with several examples of how it is used in terms of the identification of bulk fields with operators on the bound- ary of a CFT. We move on to discuss two applications of the gauge/gravity duality. The first is the application of the holographic gauge/gravity correspondence to the QCDk-string. The second applies the AdS/CFT formalism to a Kerr black hole solution embedded in 10-dimensional heterotic sting theory. These two applications of the holographic gauge/gravity duality comprise the original work presented here. We follow with summaries and discussions of the background material, the original work, and future investigations.

In this thesis we review the gauge/gravity duality and how it can be used to compute the thermodynamic properties and low-energy excitations of holographic quantum liquids - strongly-interacting field theories with a non-zero density of matter. We then study in detail the charge density excitations of two such liquids, the D3/D7 theory and the RN-AdS₄ theory, by computing the poles of their charge density Green's functions, and their charge density spectral functions. Although it is not a Landau Fermi liquid, the charge density excitations of the D3/D7 theory display many of the same properties as one, including a collisionless/hydrodynamic crossover as the temperature is increased. In contrast to this, the charge density (and energy density) excitations of the RN-AdS₄ theory do not share these properties but behave in a way that cannot be explained by Landau's theory of interacting fermionic quasiparticles. This is consistent with other results which indicate that this is not a Landau Fermi liquid.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Existem poucas dúvidas de que a QCD seja a teoria correta das interações fortes. As dificuldades em resolver a teoria em baixas energias no regime fortemente acoplado e não perturbativo tem deixado sem respostas muitas questões importantes, tais como a natureza do confinamento e o mecanismo de hadronização. Diversos métodos têm sido usados para estudar suas propriedades e consequências a baixas energias. Esses métodos incluem a QCD na rede, as equações de Dyson- Schwinger, a teoria de perturbação chiral e os modelos de quarks. Recentemente, a dualidade gauge/gravidade tem fornecido uma nova maneira de acessar o regime fortemente acoplado de uma teoria de calibre via uma teoria de gravidade dual, em especial da QCD através de modelos holográficos. Tais modelos são usualmente denominados modelos holográficos para a QCD, ou apenas modelos AdS/QCD. Nesta tese investigamos importantes problemas de interesse atual em física hadrônica envolvendo as quebras das simetrias chiral e de sabor usando modelos holográficos para a QCD. Estes problemas são: (1) o desaparecimento das constantes de decaimento leptônicas dos estados excitados do pion no limite quiral; (2) os efeitos da quebra de simetria de sabor no acoplamentos do méson rho aos mésons charmosos D and D^{*} e seus fatores de forma eletromagnéticos; (3) os efeitos de um campo magnético e da temperatura sobre o condensado quiral, sinalizando uma catálise magnética inversa.
There is little doubt that QCD is the correct theory for the strong interactions. The difficulties in solving the theory at low energies in the strongly interacting, non-perturbative regime have left unanswered many important questions, such as the nature of confinement and the mechanism of hadronization. Several approaches have been used to study its properties and consequences at low energies. These include lattice QCD, Dyson-Schwinger equations, chiral perturbation theory and quark models. More recently, the gauge/gravity duality has provided a new way to access the strongly coupled regime of a gauge theory via a dual gravity theory, in special of QCD through holographic models. Such models are usually named as holographic QCD models, or just AdS/QCD models. In this thesis, we investigate three problems of contemporary interest in hadronic physics involving the chiral and flavor symmetries holographic QCD models. These problems are: (1) the vanishing of the leptonic decay constants of the excited states of the pion in the chiral limit; (2) the effects of the flavor symmetry breaking on the strong couplings of the rho meson to the charmed D and D^{*} mesons and the their electromagnetic form factors; (3) the effects of a magnetic field and temperature on the chiral condensate, signalizing inverse magnetic catalysis.