We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for $d$-dimensional BCFTs between two nearby fixed points. We also use the AdS$_{d+1}$/BCFT$_d$ model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient RG flow both in conformal perturbation theory and the AdS$_{d+1}$/BCFT$_d$ model. In a special case, the change of the boundary entropy in the AdS$_{d+1}$/BCFT$_d$ model reduces to that of the conformal perturbation theory.
We study the response of a conserved current to external electromagnetic fields in a holographic system with boundaries using the recently proposed AdS/BCFT (boundary conformal field theory) framework. This, in particular, allows us to extract the Hall current, the Hall conductivity, plus some potentially novel transport coefficients, and relations among them. We also analyze the action of SL(2,Z) duality in the gravity bulk, which acts non-trivially on the conductivity of the BCFT. Finally we consider a type IIA string theory embedding of our setup.
We study the conductivities and entanglement structures of two different holographic gapped systems at zero density in the presence of boundaries within AdS/BCFT. The first gapped system is described by the Einstein-scalar gravity and the second one is the dual of AdS soliton geometry. We show that in both these two systems the bulk and boundary conductivities along the spatial direction of the boundary of BCFT are trivial. For the first system, when we increase the size of the subsystem the renormalized entanglement entropy is always non-negative and monotonically decreasing with discontinuou…
The holographic principle, being a generic feature of quantum gravity, should allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT correspondence, in which the dual field theory has local conformal symmetry and is defined on a manifold with boundary, is one such example. Inspired by the quotienting of AdS$_3$ by spacetime isometries in order to construct multiboundary wormholes dual to multipartite CFT$_2$ states, we find that this correspondence can be understood by combining AdS/CFT with some appropriate quotient procedure. Furthermore, in three bulk dimensions, we find …
We consider a perturbation of the Einstein gravity with the Neumann boundary condition, which is regarded as an end of the world brane (ETW brane) of the AdS/BCFT correspondence, in the AdSd+1 spaectime where d is larger than 2. We obtain the mode expansion of the perturbations explicitly for the tensionless ETW brane case. We also show that the energy-momentum tensor in a d-dimensional BCFT should satisfy nontrivial constraints other than the ones for the boundary conformal symmetry if the BCFT can couple to a d-dimensional gravity with a specific boundary condition, which can be the Neumann …
The entanglement wedge cross section in holographic picture provides a geometrical description of the entanglement for mixed states. In this paper we study the inequalities for the entanglement wedge cross section in AdS/BCFT duality. In the presence of the boundary in conformal field theory (CFT), the dual entanglement wedge cross section exhibits abundant phase structures since the extremal surface may end on the brane. We present a universal treatment which is applicable for all the possible phases such that the inequalities for the entanglement wedge cross section can be proved in an algeb…
In this paper, we study the $AdS/BCFT$ construction in $AdS_3$ and the BTZ black hole spacetime. We find a new solution to the equation for the End of the World (EoW) brane. The induced metric on this solution is that of $dS_2$ with an isometry group identical to that of $AdS_2$ and the symmetry group of the corresponding BCFT. It also leads to a corresponding EoW brane in the non-rotating BTZ background which is consistent with the periodic identifications of the non-rotating BTZ black hole. The new solution generalizes easily to higher dimensions.
We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a `boundary central charge' in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that thei…
This paper, presents the gravity duals of Conformal Field Theories with boundaries. This theory is known as AdS/BCFT correspondence. In this duality, our system has 3D gravity coupling with the Maxwell field dual to 2D BCFT. On the gravity side, we consider a 3D BTZ black hole. We analyze the effects of the chemical potential on the profile of the extra boundary for the black hole. Performing a holographic renormalization, we calculate the free energy and obtain the total entropy and corresponding area with chemical potential, and the boundary entropy for the black hole. These theories are spe…
A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of theories with boundary, which admit black hole type gravity solutions. The theories are specified by stress-energy tensors that reside on the extensions of the boundary to the bulk. From this perspective AdS/BCFT appears analogous to the fluid/gravity correspondence. Among the class of the boundary e…
We use a recently proposed holographic Kondo model as a well-understood example of AdS/boundary CFT (BCFT) duality, and show explicitly that in this model the bulk volume decreases along the RG flow. We then obtain a proof that this volume loss is indeed a generic feature of AdS/BCFT models of the type proposed by Takayanagi in 2011. According to recent proposals holographically relating bulk volume to such quantities as complexity or fidelity susceptibility in the dual field theory, this suggests the existence of a complexity or fidelity susceptibility analogue of the Affleck-Ludwig g-theorem…
We consider holographic duals of $2$-dimensional conformal field theories in the presence of a boundary, interface, defect and/or junction, referred to collectively as BCFTs. In general, the presence of a boundary reduces the $SO(2,2)$ conformal symmetry to $SO(2,1)$ and the dual geometry is realized as a warped product of the form $AdS_2 \times {\cal M}$, where ${\cal M}$ is not compact. In particular, it will contain points where the warp factor of the $AdS_2$ space diverges, leading to asymptotically $AdS_3$ regions. We show that the $AdS_2$ space-time may always be replaced with an $AdS_2$…
We study Wilson loops in string theory realizations of AdS/BCFT and wedge holography. The field theories are based on 3d $\mathcal N=4$ long quiver gauge theories engineered by D3, D5 and NS5 branes, and on BCFTs involving 4d $\mathcal N=4$ SYM coupled to such 3d theories. The holographic duals have geometry $AdS_4\times S^2\times S^2$ warped over a strip. We identify the holographic representation of antisymmetric Wilson loops associated with individual 3d gauge nodes in terms of probe D5-branes. The expectation values obtained holographically are matched to supersymmetric localization comput…
In this paper we review the AdS/BCFT proposal of T. Takayanagi for holographic description of systems with boundaries, in particular, boundary conformal field theories (BCFTs). Motivated by better understanding of the proposed duality we employ entanglement entropy as a probe of familiar properties of impurities and defects. Using the dual gravity description, we check that in two spacetime dimensions the impurity entropy does not depend on a particular state of the theory, which is a well-known CFT result. In three dimensions different, and not necessarily equivalent, definitions of the defec…
In this paper we study various dynamical aspects of the AdS/BCFT correspondence in higher dimensions. We study properties of holographic stress energy tensor by analyzing the metric perturbation in the gravity dual. We also calculate the stress energy tensor for a locally excited state on a half plane in a free scalar CFT. Both of them satisfy a reflective boundary condition that is expected for any BCFTs. We also study the behavior of the scalar field perturbation in the AdS/BCFT setup and show that they also show complete reflections. Moreover, we find that the entanglement entropy of a BCFT…
In the current study, authors present the comprehensive analysis of the Anti-de Sitter/Boundary Conformal Field Theory (AdS/BCFT) correspondence for Lovelock theory of second order in the presence of canonical (and real) scalar field non-minimally coupled to modified gravitation sector. Authors consider the special case with three dimensional BTZ (Banados-Teitelboim-Zanelli) black hole and dual 2D Conformal Field Theory with the additional boundary for higher dimensional AdS spacetime. Moreover, for the given case additional boundary profile was investigated, as well as the holographic renorma…
In this paper we study a simple gravity model dual to a (2+1)-dimensional system with a boundary at finite charge density and temperature. In our naive AdS/BCFT extension of a well known AdS/CFT system a non-zero charge density must be supported by a magnetic field. As a result, the Hall conductivity is a constant inversely proportional to the coefficients of pertinent topological terms. Since the direct conductivity vanishes, such behaviors resemble that of a quantum Hall system with Fermi energy in the gap between the Landau levels. We further analyze the properties stemming from our hologra…
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）
In this paper we construct time-dependent solutions of three-dimensional gravity in AdS space dual to systems with boundaries (BCFTs), following the AdS/BCFT prescription. Such solutions can be discussed in the context of the dynamics of first order phase transitions, or more generally, in the description of quantum quenches. As an example, we apply the holographic model to calculate the dynamics of the entanglement entropy of a local quench corresponding to a nucleation of a Euclidean bubble. As in the known 1+1 CFT examples of local cut and glue quenches, the holographic entanglement entropy…
In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.
By combining the AdS/BCFT correspondence and the brane world holography, we expect an equivalence relation between a boundary conformal field theory (BCFT) and a gravitational system coupled to a CFT. However, it still remains unclear how the boundary condition of the BCFT is translated in the gravitational system. We examine this duality relation in a two-dimensional setup by looking at the computation of entanglement entropy and energy flux conservation. We also identify the two-dimensional gravity which is dual to the boundary dynamics of a BCFT. Moreover, we show that by considering a grav…
We initiate a conformal bootstrap program to study AdS3/BCFT2 with heavy excitations. We start by solving the bootstrap equations associated with two-point functions of scalar/non-scalar primaries under the assumption that one-point functions vanish. These correspond to gravity with a brane and a non-spinning/spinning particle where the brane and the particle do not intersect with each other. From the bootstrap equations, we obtain the energy spectrum and the modified black hole threshold. We then carefully analyze the gravity duals and find the results perfectly match the BCFT analysis. In pa…
Building an AdS/BCFT Josephson junction within Horndeski gravity
Centro de Ciências Exatas, Naturais e Tecnológicas, UEMASUL（乌埃马斯ul自然科学与技术中心）；Damghan University（达姆甘大学）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）
INFN, Sezione di Torino, and Department of Physics, University of Turin（意大利国家核物理研究所都灵分部及都灵大学物理系）；Joseph Henry Laboratories, Princeton University（普林斯顿大学约瑟夫·亨利实验室）
We study the AdS/BCFT duality between two-dimensional conformal field theories with two boundaries and three-dimensional anti-de Sitter space with two Karch-Randall branes. We compute the entanglement entropy of a bipartition of the BCFT, on both the gravity side and the field theory side. At finite temperature this entanglement entropy characterizes the communication between two braneworld black holes, coupled to each other through a common bath. We find a Page curve consistent with unitarity. The gravitational result, computed using double-holographically realized quantum extremal surfaces, …
We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e. boundary conformal field theory (BCFT). Our new holography, which may be called AdS/BCFT, successfully calculates the boundary entropy or g-function in two dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g-theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.
We propose a holographic model for local quench in 1+1 dimensional Conformal Field Theory (CFT). The local quench is produced by joining two identical CFT's on semi-infinite lines. When these theories have a zero boundary entropy, we use the AdS/Boundary CFT proposal to describe this process in terms of bulk physics. Boundaries of the original CFT's are extended in AdS as dynamical surfaces. In our holographic picture these surfaces detach from the boundary and form a closed folded string which can propagate in the bulk. The dynamics of this string is governed by the tensionless Yo-Yo string s…
We study the boundary critical behavior of conformal field theories of interacting fermions in the Gross-Neveu universality class. By a Weyl transformation, the problem can be studied by placing the CFT in an anti de Sitter space background. After reviewing some aspects of free fermion theories in AdS, we use both large $N$ methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the Gross-Neveu CFT. At large $N$ and general dimension $d$, we find three distinct boundary conformal phases. Near four dimensions, where the CFT is described by the Wil…
We study the holographic entanglement entropy of spatial regions with corners in the AdS4/BCFT3 correspondence by considering three dimensional boundary conformal field theories whose boundary is a timelike plane. We compute analytically the corner function corresponding to an infinite wedge having one edge on the boundary. A relation between this corner function and the holographic one point function of the stress tensor is observed. An analytic expression for the corner function of an infinite wedge having only its tip on the boundary is also provided. This formula requires to find the globa…
We propose a new holographic dual of conformal field theory defined on a manifold with boundaries, i.e. BCFT. Our proposal can apply to general boundaries and agrees with arXiv:1105.5165 for the special case of a disk and half plane. Using the new proposal of AdS/BCFT, we successfully obtain the expected boundary Weyl anomaly and the obtained boundary central charges satisfy naturally a c-like theorem holographically. We also investigate the holographic entanglement entropy of BCFT and find that the minimal surface must be normal to the bulk spacetime boundaries when they intersect. Interestin…
In this paper, we study the logarithmic terms in the partition functions of CFTs with boundaries (BCFTs). In three dimensions, their coefficients give the boundary central charges, which are conjectured to be monotonically decreasing functions under the RG flows. We present a few supporting evidences from field theory calculations. In two dimensions, we give a holographic construction (AdS/BCFT) for an arbitrary shape of boundary and calculate its logarithmic term as well as boundary energy momentum tensors, confirming its consistency with the Weyl anomaly. Moreover, we give perturbative solut…
Indian Institute of Technology Ropar（印度技术学院罗帕尔分校）；Beijing Institute of Mathematical Sciences and Applications（北京应用数学与交叉科学研究院）；Tata Institute of Fundamental Research（塔塔基础研究所）
In this work, we study gravity duals of conformal field theories with boundaries known as AdS/BCFT correspondence, put forward by Takayanagi [1], within a scalar-tensor theory, as proposed by Horndeski in 4D [2]. We consider the case of 3D gravity dual to 2D BCFT, take a Gibbons-Hawking surface term modified by Horndeski's theory and find the corresponding 3D (BTZ) black hole solutions. We analyze the effects of Horndeski's gravity on the profile of the extra boundary for the black hole by using an approximate analytic solution. Performing a holographic renormalization, we have calculated the …
We explore some aspects of holographic dual of Boundary Conformal Field Theory (BCFT). In particular we study asymptotic symmetry of geometries which provide holographic dual of BCFTs. We also compute two-point functions of certain bosonic and fermionic operators in the dual BCFT by making use of AdS/BCFT correspondence.
In this paper, we investigate AdS/BCFT for curvature-squared gravity. To warm up, we start with Gauss-Bonnet gravity. We derive the one point function of stress tensor and show that the central charge related to the norm of displacement operator is positive for the couplings obeying causality constraints. Furthermore, by imposing the null energy condition on the end-of-the-world brane, we prove the holographic g-theorem for Gauss-Bonnet gravity. This corrects a wrong point of view in the literature, which claims that the holographic g-theorem is violated for Gauss-Bonnet gravity. As a by-produ…
We consider the effects of higher curvature terms on a holographic dual description of boundary conformal field theory. Specifically, we consider three-dimensional gravity with a specific combination of Ricci tensor square and curvature scalar square, so called, new massive gravity. We show that a boundary entropy and an entanglement entropy are given by similar expression with those of the Einstein gravity case when we introduce an {\it effective} Newton's constant and an {\it effective} cosmological constant. We also show that the holographic g-theorem still holds in this extension, and we g…
According to Witten [1], the conformal boundary condition of gravity, which specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and leads to well-defined perturbation theory of gravity about any classical solution. The conformal boundary condition was previously considered in [2, 3] in the context of AdS/BCFT, wherein the equation of motion of the end-of-the-world was derived and emphasized. In this paper, we investigate further other consequences of the conformal boundary condition in AdS/BCFT. We derive the boundary central charges of the ho…
We study the holographic entanglement entropy of spatial regions having arbitrary shapes in the AdS4/BCFT3 correspondence with static gravitational backgrounds, focusing on the subleading term with respect to the area law term in its expansion as the UV cutoff vanishes. An analytic expression depending on the unit vector normal to the minimal area surface anchored to the entangling curve is obtained. When the bulk spacetime is a part of AdS4, this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of a three dimensional …
Recently, Chapman et al. argued that holographic complexities for defects distinguish action from volume. Motivated by their work, we study complexity of quantum states in conformal field theory with boundary. In generic two-dimensional BCFT, we work on the path-integral optimization which gives one of field-theoretic definitions for the complexity. We also perform holographic computations of the complexity in Takayanagi's AdS/BCFT model following by the "complexity $=$ volume" conjecture and "complexity $=$ action" conjecture. We find that increments of the complexity due to the boundary show…
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 $Δ$-exact calculation, and we give a novel derivation of boundary entropy using the result. For the 2-poi…
Boundary flow and geometric realization in holographic $T\bar T$-deformed BCFT
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
The interpretation of semiclassical gravity as an ensemble-average of CFTs has provided much progress in understanding the factorization problem and the information paradox. In this article, we consider an averaging over boundary conditions in two-dimensional boundary conformal field theories (BCFTs). We show that the boundary averaging plays an important role not only in producing wormhole contributions but also in resolving the following problem. In general setups in AdS/BCFT, one can find unphysical solutions where branes have (self-)intersections. We show that the averaging nicely resolves…
