Motivated by extended black hole thermodynamics, we generalize the Rényi entropy of charged holographic conformal field theories (CFTs) in $d$-dimensions. Specifically, following (1807.09215), we extend the quench description of the Rényi entropy of globally charged holographic CFTs by including pressure variations of charged hyperbolically sliced anti de Sitter black holes. We provide an exhaustive analysis of the new type of charged Rényi entropy, where we find an interesting interplay between a parameter controlling the pressure of the black hole and its charge. A field theoretic interpretation of this extended charged Rényi entropy is given. In particular, in $d=2$, where the bulk geometry becomes the charged Bañados, Teitelboim, Zanelli black hole, we write down the extended charged Rényi entropy in terms of the twist operators of the charged field theory. An area law prescription for the extended Rényi entropy is formulated. We comment on several avenues for future work, including how global charge conservation relates to black hole super-entropicity.
In this paper, we develop a perturbation formulation to calculate the single interval higher spin R$\acute{e}$nyi and entanglement entropy for two dimensional conformal field theory with $\mathcal{W}_{\infty}(λ)$ symmetry. The system is at finite temperature and is deformed by higher spin chemical potential. We manage to compute higher spin R$\acute{e}$nyi entropy with various spin deformations up to order $\mathcal{O}(μ^2)$. For spin 3 deformation, we calculate exact higher spin R$\acute{e}$nyi entropy up to $\mathcal{O}(μ^4)$. When $λ=3$, in the large $c$ limit, we find perfect match with tr…
We found Bogomol'nyi type of the first order differential equations in three dimensional Einstein gravity and the effective second order ones in new massive gravity when an interacting scalar field is minimally coupled. Using these equations in Einstein gravity, we obtain analytic solutions corresponding to extremally rotating hairy black holes. We also obtain perturbatively extremal black hole solutions in new massive gravity using these lower order differential equations. All these solutions have the anti de-Sitter spaces as their asymptotic geometries and as the near horizon ones. This feat…
We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black $Dp$ branes, (ii) asymptotically Lifshitz black holes, and (iii) black $AdS$ solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutua…
We investigate the holographic superconductors immersed in an external magnetic field by using the analytical approach. We obtain the spatially dependent condensate solutions in the presence of the magnetism and find analytically that the upper critical magnetic field satisfies the relation given in the Ginzburg-Landau theory. We observe analytically the reminiscent of the Meissner effect where the magnetic field expels the condensate. Extending to the D-dimensional Gauss-Bonnet AdS black holes, we examine the influence given by the Gauss-Bonnet coupling on the condensation. Different from the…
To investigate the holography in the Karch-Randall (KR) braneworld model, we construct time-symmetric initial data of black holes floating in the bulk, and compare it with its holographic dual, which is described by four-dimensional self-gravitating quantum field theory in asymptotically AdS_4 spacetime. We also give a definition and an explicit formula of mass in the KR model extending the definition by Abbott and Deser for asymptotically AdS spacetime. We obtain supporting evidence for the holography in the KR model such as good agreements of phase structures and characteristic values betwee…
We show that there is a sector of quantum general relativity which may be expressed in a completely holographic formulation in terms of states and operators defined on a finite boundary. The space of boundary states is built out of the conformal blocks of SU(2)_L + SU(2)_R, WZW field theory on the n-punctured sphere, where n is related to the area of the boundary. The Bekenstein bound is explicitly satisfied. These results are based on a new lagrangian and hamiltonian formulation of general relativity based on a constrained Sp(4) topological field theory. The hamiltonian formalism is polynomia…
For holographic CFT states near the vacuum, entanglement entropies for spatial subsystems can be expressed perturbatively as an expansion in the one-point functions of local operators dual to light bulk fields. Using the connection between quantum Fisher information for CFT states and canonical energy for the dual spacetimes, we describe a general formula for this expansion up to second-order in the one-point functions, for an arbitrary ball-shaped region, extending the first-order result given by the entanglement first law. For two-dimensional CFTs, we use this to derive a completely explicit…
We extend the holographic Schwinger-Keldysh prescription introduced in arXiv:1812.08785 to charged black branes, with a view towards studying Hawking radiation in these backgrounds. Equivalently we study real-time fluctuations of the dual CFT held at finite temperature and finite chemical potential. We check our prescription using charged Dirac probe fields. We solve the Dirac equation in a boundary derivative expansion extending the results in arXiv:2011.07039. The Schwinger-Keldysh correlators derived using this prescription automatically satisfy the appropriate KMS relations with Fermi-Dira…
We establish an attractor mechanism for the horizon metric of asymptotically locally AdS4 supersymmetric black holes. The Kähler moduli of the metric are not fixed in the asymptotic region, however supersymmetry dictates that the near horizon metric must be the constant curvature one. We show how this mechanism is realized in detail for four-dimensional N=2 gauged supergravity coupled to vector multiplets by focusing on the STU model. A similar analysis is performed for gauged supergravity theories in five, six, and seven dimensions where we establish the same mechanism by extending previous r…
We construct a new class of entanglement measures by extending the usual definition of Renyi entropy to include a chemical potential. These charged Renyi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Renyi entropies in free field theories.
We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a chemical potential μfor the spin-three current. We show that the order μ^2 correction to the Re'nyi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. …
Extending the results of \cite{Heem}, \cite{KLRS} on the holographic representation of local gauge field operators in anti de Sitter space, here we construct the bulk operators for higher spin gauge fields in the leading order of $\frac{1}{N}$ expansion. Working in holographic gauge for higher spin gauge fields, we show that gauge field operators with integer spin $s>1$ can be represented by an integration over a ball region, which is the interior region of the spacelike bulk lightcone on the boundary. The construction is shown to be AdS-covariant up to gauge transformations, and the two-point…
We consider states of holographic conformal field theories constructed by adding sources for local operators in the Euclidean path integral, with the aim of investigating the extent to which arbitrary bulk coherent states can be represented by such Euclidean path-integrals in the CFT. We construct the associated dual Lorentzian spacetimes perturbatively in the sources. Extending earlier work, we provide explicit formulae for the Lorentzian fields to first order in the sources for general scalar field and metric perturbations in arbitrary dimensions. We check the results by holographically comp…
Based on an analysis of the entropy associated to the vacuum quantum fluctuations, we show that the holographic principle, applied to the cosmic scale, constitutes a possible explanation for the observed value of the cosmological constant, theoretically justifying a relation proposed 35 years ago by Zel'dovich. Furthermore, extending to the total energy density the conjecture by Chen and Wu, concerning the dependence of the cosmological constant on the scale factor, we show that the holographic principle may also lie at the root of the coincidence between the matter density in the universe and…
In this paper we study the Fisher information metric on the space of the coupling constants on both sides of the duality between non-relativistic dipole field theories and string theory in Schrödinger spacetime. We consider the following setup. In the gauge theory side one can deform a given conformal field theory by a proper scalar operator and compute the quantum information metric via the two-point correlation function between two such operators. On the string side the deformation corresponds to a scalar field probing the background. In the large $N$ limit of the theory the probing can be d…
We consider a holographic dual model for defect conformal field theories (DCFT) in which we include the backreaction of the defect on the dual geometry. In particular, we consider a dual gravity system in which a two-dimensional hypersurface with matter fields, the brane, is embedded into a three-dimensional asymptotically Anti-de Sitter spacetime. Motivated by recent proposals for holographic duals of boundary conformal field theories (BCFT), we assume the geometry of the brane to be determined by Israel junction conditions. We show that these conditions are intimately related to the energy c…
The Shannon based conditional entropy that underlies five-dimensional Einstein-Hilbert gravity coupled to a dilaton field is investigated in the context of dynamical holographic AdS/QCD models. Considering the UV and IR dominance limits of such AdS/QCD models, the conditional entropy is shown to shed some light onto the meson classification schemes, which corroborate with the existence of light-flavour mesons of lower spins in Nature. Our analysis is supported by a correspondence between statistical mechanics and information entropy which establishes the physical grounds to the Shannon informa…
We propose a novel mechanism to achieve superconductivity at zero chemical potential, within the holographic framework. Extending previous construction of the holographic superconductors, we consider an Einstein-Maxwell system coupled with two interacting scalars in Anti-de Sitter space. One of the scalar fields is charged and therefore, interacts non-trivially with the gauge field, while the other is uncharged. We find that, if we turn on a boundary source for the uncharged scalar field, it forces the condensation of the charged scalar, leading to a superconducting phase in the dual boundary …
The RT formula for static spacetimes arising in the AdS/CFT correspondence satisfies inequalities that are not yet proven in the case of the HRT formula, which applies to general dynamical spacetimes. Wall's maximin construction is the only known technique for extending inequalities of holographic entanglement entropy from the static to dynamical case. We show that this method currently has no further utility when dealing with inequalities for five or fewer regions. Despite this negative result, we propose the validity of one new inequality for covariant holographic entanglement entropy for fi…
We present evidence that the universal Kovtun-Son-Starinets shear viscosity to entropy density ratio of 1/4πcan be associated with a Rindler causal horizon in flat spacetime. Since there is no known holographic (gauge/gravity) duality for this spacetime, a natural microscopic explanation for this viscosity is in the peculiar properties of quantum entanglement. In particular, it is well-known that the Minkowski vacuum state is a thermal state and carries an area entanglement entropy density in the Rindler spacetime. Based on the fluctuation-dissipation theorem, we expect a similar notion of vis…
We reconsider a one-parameter class of known solutions of the circle compactification of Romans six-dimensional half-maximal supergravity. The gauge-theory duals of these solutions are confining four-dimensional field theories. Their UV completions consist of the compactification on a circle of a higher-dimensional field theory that is flowing between two fixed points in five dimensions. We systematically study the bosonic fluctuations of the supergravity theory, corresponding to the bosonic glueballs of the dual field theory. We perform numerically the calculation of the spectrum of excitatio…
During heavy ion collisions, high temperatures and strong magnetic fields are generated. We employ the gauge-gravity duality to study the N_f=2 QCD phase diagram under these extreme conditions in the quenched approximation, in particular we use the non-antipodal Sakai-Sugimoto model (SSM). We take the different coupling of up and down flavours to the magnetic field into account geometrically, resulting in a split of the chiral phase transition according to flavour. We discuss the influence of the magnetic field on the chiral temperatures -in physical GeV units- in terms of the choice of the co…
We compute the holographic entanglement entropy of a thermalized CFT on a time-dependent background in four dimensions. We consider a slab configuration extending beyond the cosmological horizon of a Friedmann-Lemaitre-Robertson-Walker metric. We identify a volume term that corresponds to the thermal entropy of the CFT, as well as terms proportional to the proper area of the entangling surface which are associated with strongly entangled degrees of freedom in the vicinity of this surface or with the expansion.
Motivated by the recent unified approach to the Smarr-like relation of AdS planar black holes in conjunction with the quasi-local formalism on conserved charges, we revisit the quantum statistical and thermodynamic relations of hairy AdS planar black holes. By extending the previous results, we identify the hairy contribution in the bulk and show that the holographic computation can be improved so that it is consistent with the bulk computation. We argue that the first law can be retained in its universal form while the relation between the on-shell renormalized Euclidean action and its free e…
We introduce a new foliation of AdS$_5$ black holes such that the conformal boundary takes the form of a $4$-dimensional FLRW spacetime with scale factor $a(t)$. The foliation employs Eddington-Finkelstein-like coordinates and is applicable to a large class of AdS black holes, supported by matter fields or not, considerably extending previous efforts in the literature. We argue that the holographic dual picture of a CFT plasma on a FLRW background provides an interesting prototype to study the nonequilibrium dynamics of expanding plasmas and use holographic renormalization to extract the renor…
Black Hole Entropy and Complexity Growth in Horndeski Gravity within the AdS/BCFT Framework
Centro de Ciências Exatas, Naturais e Tecnológicas, UEMASUL（乌埃马斯尔大学自然科学与技术科学学院）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；National Observatory of Athens（雅典国家天文台）；CAS Key Laboratory for Research in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and Technology of China（中国科学院星系与宇宙学重点实验室，中国科学技术大学天文与空间科学学院）；Universidad Católica del Norte（北天主教大学）；Damghan University（达姆甘大学）
We show how to obtain a consistent thermodynamic description of accelerating asymptotically AdS black holes, extending our previous results by including charge and rotation. We find that the key ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the `string' tensions that are responsible for the acceleration of the black hole, yielding a first law of full cohomogeneity. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard me…
Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size limit. When one of the states is the vacuum of the CFT, our result matches with the holographic entanglement entropy computations in the corresponding bulk geometries, including AdS black branes. We also discuss the first asymmetric part of the relative entropy and comment on some implications of the results on the distinguishability of black hole microstat…
We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptotically AdS spacetime and show that it carries a gravitational entropy proportional to the area of the hole. Spherical AdS-Rindler space is holographically dual to an ultraviolet sector of the boundary field theory given by restriction to a strip of finite duration in time. Because measurements have finite durations, local observers in the field theory can only access information about bounded spatial regions. We propose a notion of Residual Entropy that captures uncertainty about the state of a sys…
We investigate the possibility of using quasi-normal modes (QNMs) to probe the microscopic structure of two-dimensional (2D) anti-de Sitter (AdS$_2$) dilatonic black holes. We first extend previous results on the QNMs spectrum, found for external massless scalar perturbations, to the case of massive scalar perturbations. We find that the quasi-normal frequencies are purely imaginary and scale linearly with the overtone number. Motivated by this and extending previous results regarding Schwarzschild black holes, we propose a microscopic description of the 2D black hole in terms of a coherent st…
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 -- even in the presence of 1-loop quantum corrections to the Bekenstein-Hawking entropy formula. Then, by attributing thermodynamics to the stretche…
The thermodynamic properties of self-gravitating spherical thin matter shells an black holes in $d>4$ dimensions are studied, extending previous analysis for $d=4$. The shell joins a Minkowski interior to a Tangherlini exterior, i.e., a Schwarzschild exterior in $d$ dimensions, with $d\geqslant4$, The junction conditions alone together with the first law of thermodynamics enable one to establish that the entropy of the thin shell depends only on its own gravitational radius. Endowing the shell with a power-law temperature equation of state allows to establish a precise form for the entropy and…
