In the framework of double holography, we investigate the entanglement behavior of a brane subregion in AdS spacetime coupled to a bath on its boundary and also extract the contribution from the quantum matter within this subregion. From the boundary perspective, the brane subregion serves as the entanglement wedge of a subsystem on the conformal defect. In the ground state, we find the subsystem undergoes an entanglement phase transition induced by the degrees of freedom on the brane. With subcritical parameters, the wedge and entanglement entropy sharply decrease to zero. In contrast, in the supercritical regime, both the wedge and entropy stabilize, enabling analysis of both entanglement and reflected entropy. In this phase, we derive formulas for entanglement measures based on defect and bath central charges in the semi-classical limit. For entanglement entropy, the classical geometry only contributes a subleading term with logarithmic divergence, but the brane-bath CFT entanglement exhibits a dominant linear divergence, even in the semi-classical limit. Regarding reflected entropy within the defect subsystem, classical geometry contributes a leading term with logarithmic divergence, while the quantum matter within the entanglement wedge only contributes a finite term.
The volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and study the properties of this volume in various circumstances. We derive a formula for computing the volume for a strip entangling surface and a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the volume exhibits non-monotonic behaviour as a function of the size of the entangling region (unlike the behaviour of the entanglement entro…
We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of …
Recently, a novel formula for computing entropy in theories coupled to semi-classical gravity has been devised. Using this so-called island formula the entropy of semi-classical black holes follows a Page curve. Here, we study the relation between this novel entropy and semi-classical entropy in the context of doubly-holographic models. Double holography allows for two different $d$-dimensional descriptions of a black hole coupled to a non-gravitational bath, both of which allow a holographic computation of von Neumann entropy in bath subregions. We argue that the correct homology constraint f…
We propose that the fracton models with subsystem symmetry can be a class of toy models for the holographic principle. The discovery of the anti-de Sitter/conformal field theory correspondence as a concrete construction of holography and the subsequent developments including the subregion duality and Ryu-Takayanagi formula of entanglement entropy have revolutionized our understanding of quantum gravity and provided powerful tool sets for solving various strongly-coupled quantum field theory problems. To resolve many mysteries of holography, toy models can be very helpful. One example is the ho…
We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography can be obtained by taking the zero-volume limit of holographic defect CFT. Remarkably, it can be regarded as a holographic dual of the edge modes on the defects. For one class of solutions, we prove that the cone holography is equivalent to AdS/CFT, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the …
Double holography plays a crucial role in recent studies of Hawking radiation and information paradox by relating an intermediate picture, in which a dynamical gravity living on an end-of-the-world brane is coupled to a non-gravitational heat bath, to a much better-understood BCFT picture as well as a bulk picture. In this paper, causal structures in generic double holographic setups are studied. We find that the causal structure in the bulk picture is compatible with causality in the BCFT picture, thanks to a generalization of the Gao-Wald theorem. On the other hand, consistency with the bulk…
In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of th…
In the twisted M-theory setting, various types of fusion of M2 and M5 branes induce coproducts between the algebra of operators on M2 branes and the algebra of operators on M5 branes. By doing a perturbative computation in the gravity side, which is captured by the 5d topological holomorphic $U(1)$ Chern-Simons theory, we reproduce the non-perturbative coproducts.
Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual theory. In this paper, we describe how changes in the entanglement due to a local projective measurement (LPM) on a subregion $A$ of the boundary theory modify the bulk dual spacetime. We find that LPMs destroy portions of the bulk geometry, yielding post-measurement bulk spacetimes dual to the complementary unmeasured region $A^c$ that are cut off by end-of-the-world branes. Using a bulk calculation in $AdS_3$ and tensor network models of holography, we show that the portion…
We formulate a version of the information paradox in de Sitter spacetime and show that it is solved by the emergence of entanglement islands in the context of the DS/dS correspondence; in particular, the entanglement entropy of a subregion obeys a time-dependent Page curve. Our construction works in general spacetime dimensions and keeps the graviton massless. We interpret the resulting behavior of the entanglement entropy using double holography. It suggests that the spatial distribution of microscopic degrees of freedom depends on descriptions, as in the case of a black hole. In the static (…
We study codimension-even conical defects that contain a deficit solid angle around each point along the defect. We show that they lead to a delta function contribution to the Lovelock scalar 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 h…
We study conical geometry with the maximal number of fermionic symmetry in the higher spin supergravity described by sl(N+1|N) + sl(N+1|N) Chern-Simons gauge theory. It was proposed that a three dimensional N=2 higher spin supergravity is holographically dual to the N=(2,2) CP^N Kazama-Suzuki model. Based one the duality, we find a map between conical geometries and primary states in the dual CFT. In particular, we construct geometric solutions corresponding to primary states in the RR-sector. The proposal is checked by the comparison of a few charges and by the relation between null vectors a…
We examine the formation and critical dynamics of topological defects via Kibble-Zurek mechanism in a (2+1)-dimensional quantum critical point, which is conjectured to dual to a Lifshitz geometry. Quantized magnetic fluxoids are spontaneously generated and trapped in the cores of order parameter vortices, which is a feature of type II superconductors. Time evolution of the average condensate is found to lag behind the instantaneous equilibrium value of the order parameter, a typical phenomenon in nonequilibrium dynamics. Scalings of vortex number density and the "freeze-out" time match the pre…
We model the back-reaction of a static observer in four-dimensional de Sitter spacetime by means of a singular $\mathbb Z_q$ quotient. The set of fixed points of the $\mathbb Z_q$ action consists of a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. The introduction of an orbifold parameter $q>1$ permits the construction of an effective action for the bulk gravity theory with support on each of these minimal surfaces. The effective action corresponds to that of Liouville field theory on a 2-sphere with a finite vacuum expectation value of the Liouville fie…
We discuss classification of defects of various codimensions within a holographic model of pure Yang-Mills theories or gauge theories with fundamental matter. We focus on their role below and above the phase transition point as well as their weights in the partition function. The general result is that objects which are stable and heavy in one phase are becoming very light (tensionless) in the other phase. We argue that the $θ$ dependence of the partition function drastically changes at the phase transition point, and therefore it correlates with stability properties of configurations. Some po…
We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT (BCFT) or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi-)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For BCFTs and…
Central South University（中南大学）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Freie Universität Berlin（柏林自由大学）
Does gravity constrain computation? We study this question using the AdS/CFT correspondence, where computation in the presence of gravity can be related to non-gravitational physics in the boundary theory. In AdS/CFT, computations which happen locally in the bulk are implemented in a particular non-local form in the boundary, which in general requires distributed entanglement. In more detail, we recall that for a large class of bulk subregions the area of a surface called the ridge is equal to the mutual information available in the boundary to perform the computation non-locally. We then argu…
We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel "defect superconformal field theory" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction …
We study the dynamic after a smooth quench across a continuous transition from the disordered phase to the ordered phase. Based on scaling ideas, linear response and the spectrum of unstable modes, we develop a theoretical framework, valid for any second order phase transition, for the early-time evolution of the condensate in the broken phase. Our analysis unveils a novel period of non-adiabatic evolution after the system passes through the phase transition, where a parametrically large amount of coarsening occurs before a well-defined condensate forms. Our formalism predicts a rate of defect…
Partial reduction is a Randall-Sundrum reduction for only part of the AdS region between finite tension brane and zero tension brane. This is interesting in AdS/BCFT where the AdS bulk contains a defect brane. We employ partial reduction for a AdS bulk with a brane evolving as a $2d$ Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalence between defect extremal surface and island formula for a large subregion fine grained entropy in boundary CFT. We then move to higher dimensions and demonstrate the existence of $4d$ massless graviton on AdS$_4$ brane in partial reduction. …
We investigate relevant deformation and the renormalization group flow in a defect conformal field theory from the point of view of the holography. We propose a candidate of g-function in the context of the holography, and prove the g-theorem: the g-function is monotonically non-increasing along the RG flow. We apply this g-theorem to the D5-brane solution which is an asymptotically AdS_4 x S^2 brane in AdS_5 x S^5. This solution corresponds to the mass deformation of the defect CFT. We checked that the g-function is monotonically non-increasing in this solution.
