Conical defects and holography in topological AdS gravity

We study codimension-even conical defects that contain a deficit solid angle around each point along the defect. We show that they lead to delta function contributions to Lovelock scalars and we compute the contribution by two methods. We then show that these codimension-even defects appear as Euclidean brane solutions in higher dimensional topological AdS gravity which is Lovelock-Chern-Simons gravity without torsion. The theory possesses a holographic Weyl anomaly that is purely of type-A and proportional to the Lovelock scalar. Using the formula for the defect contribution, we prove a holographic duality between codimension-even defect partition functions and codimension-even brane on-shell actions in Euclidean signature. More specifically, we find that the logarithmic divergences match, because the Lovelock-Chern-Simons action localizes on the brane exactly. We demonstrate the duality explicitly for a spherical defect on the boundary which extends as a codimension-even hyperbolic brane into the bulk. For vanishing brane tension, the geometry is a foliation of Euclidean AdS space that provides a one-parameter generalization of AdS-Rindler space.Peer reviewe

Structure of holographic BCFT correlators from geodesics

We compute correlation functions, specifically 1-point and 2-point functions, in holographic boundary conformal field theory (BCFT) using geodesic approximation. The holographic model consists of a massive scalar field coupled to a Karch-Randall brane-a rigid boundary in the bulk AdS space. Geodesic approximation requires the inclusion of paths reflecting off of this brane, which we show in detail. For the 1-point function, we find agreement between geodesic approximation and the harder Delta-exact calculation, and we give a novel derivation of boundary entropy using the result. For the 2-point function, we find a factorization phase transition and a mysterious set of anomalous boundary-localized BCFT operators. We also discuss some puzzles concerning these operators.Peer reviewe

Quasi-local energy and ADM mass in pure Lovelock gravity

We study how the standard definitions of ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. The quasi-local energy is renormalized using the background subtraction prescription and we consider its limit for large surfaces. We find that the large surface limit vanishes for asymptotically flat fall-off conditions except in Einstein gravity. This problem is avoided by focusing on the variation of the quasi-local energy which correctly approaches the variation of the ADM mass for large surfaces. As a result, we obtain a new simple formula for the ADM mass in pure Lovelock gravity. We apply the formula to spherically symmetric geometries verifying previous calculations in the literature. We also revisit asymptotically AdS geometries.Peer reviewe

Flavored ABJM theory on the sphere and holographic F-functions

We study strongly coupled ABJM theory on the 3-sphere with massive quenched flavor using the AdS/CFT correspondence. The holographic dual consists of type IIA supergravity with probe D6-branes. The flavor mass is a relevant deformation driving an RG flow whose IR endpoint is pure ABJM theory. At non-zero mass, we find that the theory on the 3-sphere exhibits a quantum phase transition at a critical value of the sphere radius. The transition corresponds to a topology change in the D6-brane embeddings whose dual interpretation is the meson-melting transition. We perform the holographic computation of the free energy on 3-sphere and we use it to construct various candidate F-functions. These were recently proposed in the context of Einstein-scalar gravity to interpolate monotonically between the values of the sphere free energies of the UV and IR CFTs. We find that while the F-functions of the flavored ABJM theory have the correct UV and IR limits, they are not monotonic. We surmise that the non-monotonicity is related to the presence of the phase transition.Peer reviewe

Holographic BCFT Spectra from Brane Mergers

We use holography to study the spectra of boundary conformal field theories (BCFTs). To do so, we consider a 2-dimensional Euclidean BCFT with two circular boundaries that correspond to dynamical end-of-the-world branes in 3-dimensional gravity. Interactions between these branes inform the operator content and the energy spectrum of the dual BCFT. As a proof of concept, we first consider two highly separated branes whose only interaction is taken to be mediated by a scalar field. The holographic computation of the scalar-mediated exchange reproduces a light scalar primary and its global descendants in the closed-string channel of the dual BCFT. We then consider a gravity model with point particles. Here, the interaction of two separated branes corresponds to a heavy closed-string operator which lies below the black hole threshold. However, we may also consider branes at finite separation that "merge" non-smoothly. Such brane mergers can be used to describe unitary sub-threshold boundary-condition-changing operators in the open-string spectrum of the BCFT. We also find a new class of sub-threshold Euclidean bra-ket wormhole saddles with a factorization puzzle for closed-string amplitudes.Comment: 53 pages (including appendices) + references, 23 figures; v2: added details to bra-ket wormhole discussion, added reference

Quantum information geometry of driven CFTs

Driven quantum systems exhibit a large variety of interesting and sometimes exotic phenomena. Of particular interest are driven conformal field theories (CFTs) which describe quantum many-body systems at criticality. In this paper, we develop both a spacetime and a quantum information geometry perspective on driven 2d CFTs. We show that for a large class of driving protocols the theories admit an alternative but equivalent formulation in terms of a CFT defined on a spacetime with a time-dependent metric. We prove this equivalence both in the operator formulation as well as in the path integral description of the theory. A complementary quantum information geometric perspective for driven 2d CFTs employs the so-called Bogoliubov-Kubo-Mori (BKM) metric, which is the counterpart of the Fisher metric of classical information theory, and which is obtained from a perturbative expansion of relative entropy. We compute the BKM metric for the universal sector of Virasoro excitations of a thermal state, which captures a large class of driving protocols, and find it to be a useful tool to classify and characterize different types of driving. For M\"obius driving by the SL(2,R) subgroup, the BKM metric becomes the hyperbolic metric on the unit disk. We show how the non-trivial dynamics of Floquet driven CFTs is encoded in the BKM geometry via M\"obius transformations. This allows us to identify ergodic and non-ergodic regimes in the driving. We also explain how holographic driven CFTs are dual to driven BTZ black holes with evolving horizons. The deformation of the black hole horizon towards and away from the asymptotic boundary provides a holographic understanding of heating and cooling in Floquet CFTs.Comment: 82 pages including references, 14 figure

Quantum hypothesis testing in many-body systems

Peer reviewe

Einstein's equations from entanglement entropy

Since the inception of the AdS/CFT correspondence in 1997 there has been great interest in the holographic description of quantum gravity in terms of conformal field theory. Studying how classical gravity emerges in this framework helps us to understand the quantum foundations of general relativity. A fundamental concept is entanglement entropy which has a classical interpretation in terms of areas of minimal surfaces in general relativity, due to Ryu and Takayanagi. This thesis is a review on how Einstein's equations can be derived up to second order from the Ryu-Takayanagi formula in the context of AdS/CFT correspondence. It also serves as an introduction to entanglement entropy in quantum field theories and holography, while providing necessary mathematical ingredients to understand the derivation. We also review a related derivation, based on the entanglement equilibrium hypothesis, and discuss its extensions to higher order theories of gravity

Études des bords et des branes dans la dualité holographique

Quantum conformal field theory (CFT) is a special type of quantum field theory which is symmetric under conformal transformations of spacetime. Because of their relative simplicity, CFTs appear in many different areas of theoretical physics such as condensed matter physics and quantum gravity. For example in the study of statistical mechanical systems, CFTs appear as continuum effective descriptions of collective phenomena near a critical point where a phase transition occurs. In this context, the existence of different types of CFTs is connected to the classification of different universality classes of phase transitions. As theories by themselves, CFTs do not describe the gravitational force which is transmitted by the graviton particle. However, CFTs are deeply connected to gravity in string theory where they determine the dynamics of quantum mechanical strings. The spectrum of vibrational modes of a string include the graviton making string theory a theory of quantum gravity which is self-consistent based on vast theoretical knowledge. Hence CFTs have played a central role in the development of string theory and in our quest to unify Einstein's theory of gravity with quantum mechanics. The main milestone in the modern understanding of quantum gravity was the discovery of the holographic duality in string theory. Simply put, the duality says that there exist special CFTs which contain rules to describe gravity hidden in them. However, these rules are holographic, because they describe gravity in a spacetime with one extra dimension: the duality is like a hologram where a three-dimensional image (gravity) is encoded on a two-dimensional surface (CFT). Not only is the holographic duality useful in understanding the structure of quantum gravity, it is also extremely powerful in predicting dynamics of strongly interacting quantum fields that occur inside neutron stars for example. This thesis is devoted to the study of the holographic duality and it is based on four research articles on the topic. The focus is on how extended objects, namely boundaries and branes, behave on both sides of the duality. In string theory, boundaries of open strings describe dynamics of D-branes whose understanding was crucial for the discovery of the holographic duality in the first place. Similarly on the CFT side, boundaries give raise to observable effects such as the Casimir effect when the system is confined between two parallel plates. The goal of the thesis is to give an introduction to these concepts in the context of the holographic duality.Une théorie quantique des champs est conforme lorsqu'elle est symétrique sous les transformations conforme de l'espace-temps. En raison de leur relative simplicité, les CFT apparaissent dans de nombreux domaines de la physique théorique tels que la physique de la matière condensée et la gravité quantique. Par exemple, dans l'étude des systèmes de mécanique statistique, les CFT apparaissent comme des descriptions effectives dans le limite du continu de phénomènes collectifs près d'un point critique où une transition de phase se produit. Dans ce contexte, l'existence de différents types de CFT est liée à la classification de différentes classes d'universalité de transitions de phase. En tant que théories en elles-mêmes, les CFT ne décrivent pas la force gravitationnelle qui est transmise par la particule graviton. Cependant, les CFT sont profondément liées à la gravité dans la théorie des cordes où elles déterminent la dynamique des cordes quantiques. Le spectre des modes de vibration d'une corde comprend le graviton, ce qui fait de la théorie des cordes une théorie de la gravité quantique cohérente et s'appuie sur de vastes connaissances théoriques. Ainsi, les CFT ont joué un rôle central dans le développement de la théorie des cordes et dans notre quête pour unifier la théorie de la gravité d'Einstein avec la mécanique quantique. La principale étape dans la compréhension moderne de la gravité quantique a été la découverte de la dualité holographique dans la théorie des cordes. En termes simples, la dualité énonce que certaines CFT contiennent des règles pour décrire la gravité cachées en elles. Cependant, ces règles sont holographiques car elles décrivent la gravité dans un espace-temps avec une dimension supplémentaire : la dualité est comme un hologramme où une image tridimensionnelle (la gravité) est encodée sur une surface bidimensionnelle (CFT). Non seulement la dualité holographique est utile pour comprendre la structure de la gravité quantique, elle est également extrêmement puissante pour prédire la dynamique de champs quantiques fortement couplés qui se produisent, par exemple, à l'intérieur des étoiles à neutrons. Cette thèse est consacrée à l'étude de la dualité holographique et est basée sur quatre articles de recherche sur le sujet. L'accent est mis sur la manière dont les objets étendus, à savoir les bords et les branes, se comportent des deux côtés de la dualité. Dans la théorie des cordes, les bords des cordes ouvertes décrivent la dynamique des D-branes dont la compréhension a été cruciale pour la découverte de la dualité holographique en premier lieu. De même, du côté des CFT, les bords donnent lieu à des effets observables tels que l'effet Casimir lorsque le système est confiné entre deux plaques parallèles. L'objectif de la thèse est de donner une introduction à ces concepts dans le contexte de la dualité holographique

Études des bords et des branes dans la dualité holographique

Quantum conformal field theory (CFT) is a special type of quantum field theory which is symmetric under conformal transformations of spacetime. Because of their relative simplicity, CFTs appear in many different areas of theoretical physics such as condensed matter physics and quantum gravity. For example in the study of statistical mechanical systems, CFTs appear as continuum effective descriptions of collective phenomena near a critical point where a phase transition occurs. In this context, the existence of different types of CFTs is connected to the classification of different universality classes of phase transitions. As theories by themselves, CFTs do not describe the gravitational force which is transmitted by the graviton particle. However, CFTs are deeply connected to gravity in string theory where they determine the dynamics of quantum mechanical strings. The spectrum of vibrational modes of a string include the graviton making string theory a theory of quantum gravity which is self-consistent based on vast theoretical knowledge. Hence CFTs have played a central role in the development of string theory and in our quest to unify Einstein's theory of gravity with quantum mechanics. The main milestone in the modern understanding of quantum gravity was the discovery of the holographic duality in string theory. Simply put, the duality says that there exist special CFTs which contain rules to describe gravity hidden in them. However, these rules are holographic, because they describe gravity in a spacetime with one extra dimension: the duality is like a hologram where a three-dimensional image (gravity) is encoded on a two-dimensional surface (CFT). Not only is the holographic duality useful in understanding the structure of quantum gravity, it is also extremely powerful in predicting dynamics of strongly interacting quantum fields that occur inside neutron stars for example. This thesis is devoted to the study of the holographic duality and it is based on four research articles on the topic. The focus is on how extended objects, namely boundaries and branes, behave on both sides of the duality. In string theory, boundaries of open strings describe dynamics of D-branes whose understanding was crucial for the discovery of the holographic duality in the first place. Similarly on the CFT side, boundaries give raise to observable effects such as the Casimir effect when the system is confined between two parallel plates. The goal of the thesis is to give an introduction to these concepts in the context of the holographic duality.Une théorie quantique des champs est conforme lorsqu'elle est symétrique sous les transformations conforme de l'espace-temps. En raison de leur relative simplicité, les CFT apparaissent dans de nombreux domaines de la physique théorique tels que la physique de la matière condensée et la gravité quantique. Par exemple, dans l'étude des systèmes de mécanique statistique, les CFT apparaissent comme des descriptions effectives dans le limite du continu de phénomènes collectifs près d'un point critique où une transition de phase se produit. Dans ce contexte, l'existence de différents types de CFT est liée à la classification de différentes classes d'universalité de transitions de phase. En tant que théories en elles-mêmes, les CFT ne décrivent pas la force gravitationnelle qui est transmise par la particule graviton. Cependant, les CFT sont profondément liées à la gravité dans la théorie des cordes où elles déterminent la dynamique des cordes quantiques. Le spectre des modes de vibration d'une corde comprend le graviton, ce qui fait de la théorie des cordes une théorie de la gravité quantique cohérente et s'appuie sur de vastes connaissances théoriques. Ainsi, les CFT ont joué un rôle central dans le développement de la théorie des cordes et dans notre quête pour unifier la théorie de la gravité d'Einstein avec la mécanique quantique. La principale étape dans la compréhension moderne de la gravité quantique a été la découverte de la dualité holographique dans la théorie des cordes. En termes simples, la dualité énonce que certaines CFT contiennent des règles pour décrire la gravité cachées en elles. Cependant, ces règles sont holographiques car elles décrivent la gravité dans un espace-temps avec une dimension supplémentaire : la dualité est comme un hologramme où une image tridimensionnelle (la gravité) est encodée sur une surface bidimensionnelle (CFT). Non seulement la dualité holographique est utile pour comprendre la structure de la gravité quantique, elle est également extrêmement puissante pour prédire la dynamique de champs quantiques fortement couplés qui se produisent, par exemple, à l'intérieur des étoiles à neutrons. Cette thèse est consacrée à l'étude de la dualité holographique et est basée sur quatre articles de recherche sur le sujet. L'accent est mis sur la manière dont les objets étendus, à savoir les bords et les branes, se comportent des deux côtés de la dualité. Dans la théorie des cordes, les bords des cordes ouvertes décrivent la dynamique des D-branes dont la compréhension a été cruciale pour la découverte de la dualité holographique en premier lieu. De même, du côté des CFT, les bords donnent lieu à des effets observables tels que l'effet Casimir lorsque le système est confiné entre deux plaques parallèles. L'objectif de la thèse est de donner une introduction à ces concepts dans le contexte de la dualité holographique