We propose a candidate $c$-function in arbitrary dimensional quantum field theories with broken Lorentz and rotational symmetry. For holographic theories we derive the necessary and sufficient conditions on the geometric background for these $c$-functions to satisfy the $c$-theorem. We obtain the null energy conditions for anisotropic background to show that do not themselves assure the $c$-theorem. By employing them, we find that is possible to impose conditions on the UV data that are enough to guarantee at least one monotonic $c$-function along the RG flow. These UV conditions can be used as building blocks for the construction of anisotropic monotonic RG flows. Finally, we apply our results to several known anisotropic theories and identify the region in the parameters space of the metric where the $c$-theorem holds for our proposed $c$-function.
In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting $\mathcal{N}=4$ super Yang-Mills theories by introducing a minimal surface in the S$^5$ direction, instead of the AdS$_5$ direction. This offers a possible general…
We compute the holographic entanglement entropy in the gravity with higher curvature terms dual to d=4 N=2 SCFTs in F-theory using the method proposed in arXiv:1011.5819. The log term of this entanglement entropy reproduces the A-type anomaly of the dual SCFTs in F- theory using the gravity dual with the higher derivative term, which, using the field redefinition, can be transformed to the Gauss-Bonnet term in the subleading order of a derivative expansion. Our analysis shows that the 1/N^2 correction for the central charges should be produced from the gravity including higher derivative terms…
We review classical results on holographic entanglement entropy utilizing the Hamilton-Jacobi approach. Possibility of using the entanglement entropy as a probe of confinement is shortly discussed in the context of lattice data.
We study properties of the minimal cross section of entanglement wedge which connects two disconnected subsystems in holography. In particular we focus on various inequalities which are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heuristic argument which supports this identification based on a tensor network interpretation of holography. This implies that the entanglement of purification satisfies the strong superadditivity for holograp…
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large $N$ limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large $N$ limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse sp…
Holographic entanglement entropy quantities for a three-party system are considered, namely tripartite information, total correlation and secrecy monotone. A holographic approach with Vaidya-AdS is used to calculate time evolution of the entanglement entropy during non-equilibrium heating. We study time dependence of these three entropy quantities.
We study the holographic entanglement entropy in a (d+1)-dimensional boundary quantum field theory at both the zero and finite temperature. The phase diagrams for the holographic entanglement entropy at various temperatures are obtained by solving the entangled surfaces in the different homology. We also verify the Araki-Lieb inequality and illustrate the entanglement plateau.
We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the entanglement wedge in holographic codes with a quantum correction term equal to the logarithmic negativity between the bulk degrees of freedom on either side of the entanglement wedge cross section. This leads us to conjecture a holographic dual for logarithmic negativity that is related to the area of a cosmic brane with tension in the entanglement wedge plus a quantum correction term. This is closely relat…
In this note we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region ${\cal A}$ lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and CFT calculation of the entanglement entropy.
We study holographic entanglement entropy in spatially anisotropic field theory. We observe that for the background we consider in this paper, to a good approximation, the holographic entanglement entropy can be decomposed into two terms. One of them is the entanglement entropy of the isotropic field theory at fixed temperature and the other term is only a function of anisotropy parameter. Moreover, for large enough values of anisotropy parameter, our numerical results indicate that the entanglement entropy in the perpendicular direction to anisotropic direction is greater than the parallel ca…
The entanglement entropy of various geometries is calculated for the boundary theory dual to a stack of N Dp-branes. The entanglement entropies are readily expressed in terms of the effective coupling at the appropriate energy scales. The results are also compared to the entropy density of a black brane and some universal properties of holographic entropy are found.
We study the holographic entanglement measures such as the holographic mutual information, HMI, and the holographic entanglement of purification, EoP, in a holographic QCD model at finite temperature and zero chemical potential. This model can realize various types of phase transitions including crossover, first order and second order phase transitions. We use the HMI and EoP to probe the phase structure of this model and we find that at the critical temperature they can characterize the phase structure of the model. Moreover we obtain the critical exponent using the HMI and EoP.
We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.
Using the proposal for holographic entanglement entropy in higher derivative gravities, we compute holographic entanglement entropy for the conformal gravity in four dimensions which turns out to be finite. However, if one subtracts the contribution of the four dimensional Gauss-Bonnet term, the corresponding entanglement entropy has a divergent term and indeed restricted to an Einstein solution of the conformal gravity, the resultant entanglement entropy is exactly the same as that in the Einstein gravity. We will also make a comment on the first law of the entanglement thermodynamics for the…
The holographic entanglement entropy (HEE) is investigated for a black hole under the minimal geometric deformation (MGD) procedure, created by gravitational decoupling via an anisotropic fluid, in an AdS/CFT on the brane setup. The respective HEE corrections are computed and confronted to the corresponding corrections for both the standard MGD black holes and the Schwarzschild ones.
We study the entanglement contour, a quasi-local measure of entanglement, and propose a generic formula for the contour in 1+1d quantum systems. We use this formalism to investigate the real space entanglement structure of various static CFTs as well as local and global quantum quenches. The global quench elucidates the spatial distribution of entanglement entropy in strongly interacting CFTs and clarifies the interpretation of the entanglement tsunami picture. The entanglement tsunami effectively characterizes the non-local growth of entanglement entropy while the contour characterizes the lo…
We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a s…
From the perspective of AdS/CFT correspondence, we study the gravitational Chern-Simons term correction to the holographic entanglement entropy of CFT on the conformal boundary of asymptotically AdS$_3$ spacetime using the off-shell Euclidean path integral method. We show that, like the BTZ black hole entropy, the holographic entanglement entropy is indeed modified due to the gravitational Chern-Simons term although the bulk geometry does not change.
We study the entanglement entropy of general holographic dual models both in AdS soliton and AdS black hole backgrounds with full backreaction. We find that the entanglement entropy is a good probe to explore the properties of the holographic superconductors and provides richer physics in the phase transition. We obtain the effects of the scalar mass, model parameter and backreaction on the entropy, and argue that the jump of the entanglement entropy may be a quite general feature for the first order phase transition. In strong contrast to the insulator/superconductor system, we note that the …
We study the holographic entanglement entropy under small deformations of AdS, including time-dependence. It is found through perturbative analysis that the divergent terms are not affected and the change appears only in the finite terms. We also consider the entanglement thermodynamic first law, and calculate the entanglement temperature and confirm that it is inversely proportional to the size of the entangling region.
In this paper we study the holographic entanglement entropy in a large N noncommutative gauge field theory with two $θ$ parameters by Ryu-Takayanagi prescription (RT-formula). We discuss what contributions the presence of noncommutativity will make to the entanglement entropy in two different circumstances: 1) a rectangular strip and 2) a cylinder. Since we want to investigate the entanglement entropy only, we will not be discussing the finite temperature case in which the entropy calculated by the area of minimal surface will largely be the thermal part rather than the entanglement part. We f…
In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
The holographic superconductors, as one of the most important application of gauge/gravity duality, promote the study of strongly coupled superconductors via classical general relativity living in one higher dimension. One of the interesting properties in holographic superconductor is the appearance of first and second order phase transitions. Recently, another active studies in holographic framework is the holographic entanglement entropy and complexity evaluated from gravity side. In this note, we study the properties of the holographic entanglement entropy and complexity crossing both first…
Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy in terms of a certain integral over the entangling surface. This easily generalizes to any bulk codimension-$p$ extremal surface. We study additional properties of bulk codimension-$p$ extremal surfaces corresponding to strip/plane "entangling surfaces" in various geometries. We compute universal terms for codim-one volumes (conjectured to be dual to hologr…
Entanglement entropy is a useful probe of compressible quantum matter because it can detect the existence of Fermi surfaces, both of microscopic fermionic degrees of freedom and of "hidden" gauge charged fermions. Much recent attention has focused on holographic efforts to model strongly interacting compressible matter of interest for condensed matter physics. We complete the entanglement analysis initiated in Huijse {\em et al.}, Phys. Rev. B 85, 035121 (2012) (arXiv:1112.0573) and Ogawa {\em et al.}, JHEP 1, 125 (2012) (arXiv:1111.1023) using the recent proposal of Faulkner {\em et al.} (arX…
We first calculate the jet quenching parameter of an anisotropic plasma with a U(1) chemical potential via the AdS/CFT duality. The effects of charge, anisotropy parameter and quark motion direction on the jet quenching parameter are investigated. We then discuss the situation of anisotropic black brane in the IR region. We study both the jet quenching parameters along the longitudinal direction and transverse plane.
We study corner contributions to holographic entanglement entropy in non-conformal backgrounds: a kink for D2-branes as well as a cone and two different types of crease for D4-branes. Unlike 2+1-dimensional CFTs, the corner contribution to the holographic entanglement entropy of D2-branes exhibits a power law behaviour rather than a logarithmic term. However, the logarithmic term emerges in the holographic entanglement entropy of D4-branes. We identify the logarithmic term for a cone in D4-brane background as the universal contribution under appropriate limits and compare it with other physica…
Using holographic entanglement entropy for strip geometry, we construct a candidate for a c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not suf…
In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We disclose the properties of phases mostly from the holographic topological entanglement entropy of the system. We find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. The behaviors of entanglement entropy at large strip size suggest that the area law still holds with dark matter sector. We also conclude that the holographic topological entanglement entropy is useful i…
We studied entanglement entropy for a time dependent two dimensional holographic superconductor. We showed that the conserved charge of the system plays the role of the critical parameter to have condensation.
We discuss the behaviour of holographic entanglement entropy following a local quench in 2+1 dimensional strongly coupled CFTs. The entanglement generated by the quench propagates along an emergent light-cone, reminiscent of the Lieb-Robinson light-cone propagation of correlations in non-relativistic systems. We find the speed of propagation is bounded from below by the entanglement tsunami velocity obtained earlier for global quenches in holographic systems, and from above by the speed of light. The former is realized for sufficiently broad quenches, while the latter pertains for well localiz…
In this paper, we show that a higher derivative theory, such as New Massive Gravity, allows the existence of new entangling surfaces with non-zero extrinsic curvature. We perform the analysis for Lifshitz and Warped $AdS$ space times, revealing the role of the higher derivative contributions in the calculation of the holographic entanglement entropy. Finally, as an outcome of our holographic analysis we briefly comment on the dual boundary theory.
The entanglement entropy has been historically studied by many authors in order to obtain quantum mechanical interpretations of the gravitational entropy. The discovery of AdS/CFT correspondence leads to the idea of holographic entanglement entropy, which is a clear solution to this important problem in gravity. In this article, we would like to give a quick survey of recent progresses on the holographic entanglement entropy. We focus on its gravitational aspects, so that it is comprehensible to those who are familiar with general relativity and basics of quantum field theory.
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-d…
We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional dual conformal field theories through the $AdS/CFT$ correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature ($1+1$)-dimensional holographic conformal field the…
The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $Σ$ with boundary $\partialΣ$ is an exact holographic mapping similar to the proposal in arXiv:1309.6282. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region $A$ and its complement $\bar{A}$ are specified on the boundary $\partialΣ$, we sho…
In arXiv:1601.02634 it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS$_3$ (WAdS$_3$) with Dirichlet boundary conditions. In this paper, we consider AdS$_3$ and WAdS$_3$ with Dirichlet-Neumann boundary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and Rényi entropy using AdS$_3$/WCFT and WAdS$…
Using a uniformization map we determine the holographic entanglement entropy for states of a Warped Conformal Field Theory dual to a generic vacuum metric in AdS$_3$ gravity with Compère--Song--Strominger boundary conditions. We point out how that expression could lead to inequalities that can be interpreted as quantum energy conditions for Warped Conformal Field Theories.
We propose a covariant holographic conjecture for the entanglement negativity of mixed states in bipartite systems described by $d$-dimensional conformal field theories dual to bulk non static $AdS_{d+1}$ configurations. Application of our conjecture to $(1+1)$-dimensional conformal field theories dual to bulk rotating BTZ black holes exactly reproduces the corresponding entanglement negativity in the large central charge limit and characterizes the distillable entanglement. We further demonstrate that our conjecture applied to the case of bulk extremal rotating BTZ black holes also characteri…
We compute the holographic entanglement entropy contribution from planar two-dimensional defects in six-dimensional $\mathcal{N}=(2,0)$ superconformal field theory, holographically dual to probe M2- and M5-branes in $AdS_7 \times S^4$. In particular, we test the viability of the universal contribution of the defect to entanglement entropy as a candidate $C$-function. We find that this coefficient is not monotonic under defect renormalization group flows triggered by the vacuum expectation value of a marginal operator. Another candidate $C$-function, the on-shell action inside the entanglement …
We study the application of our recent holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with a conserved charge. In this context we obtain the holographic entanglement negativity for zero and finite temperature mixed state configurations in $d$-dimensional conformal field theories dual to bulk extremal and non extremal charged $AdS_{d+1}$ black holes. Our results conform to quantum information theory expectations and constitute significant consistency checks for our conjecture.
Recent work has shown that entanglement and the structure of spacetime are intimately related. One way to investigate this is to begin with an entanglement entropy in a conformal field theory (CFT) and use the AdS/CFT correspondence to calculate the bulk metric. We perform this calculation for ABJM, a particular 3-dimensional supersymmetric CFT (SCFT), in its ground state. In particular we are able to reconstruct the pure AdS4 metric from the holographic entanglement entropy of the boundary ABJM theory in its ground state. Moreover, we are able to predict the correct AdS radius purely from ent…
In this paper, we study the entanglement contour in a general excited state in the holographic 2d CFT using the partial entanglement entropy proposal. We show how thermodynamics fixes the entanglement contour relating it to the first law of entanglement. We derive the entanglement contour for a general time-dependent excited state and consider a quenched initial state in the presence of spatial boundaries as an explicit example. Finally, we comment on the coarse-graining and the complexity contour in the $AdS_3/CFT_2$.
We argue that Landau-Fermi liquids do not have any gravity duals in the purely classical limit. We employ the logarithmic behavior of entanglement entropy to characterize the existence of Fermi surfaces. By imposing the null energy condition, we show that the specific heat always behaves anomalously. We also present a classical gravity dual which has the expected behavior of the entanglement entropy and specific heat for non-Fermi liquids.
In this work, we study the holographic entanglement entropy of two dimensional $T\bar{T}$-deformed conformal field theory. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of New massive gravity, General minimal massive gravity, and Exotic general massive gravity. We also apply Song's prescription to obtain the entanglement entropy for deformed theories. In each cases, we find agreement between the results.
We show that Schwarzschild black hole metrics are, asymptotically, Weyl equivalent to $AdS_2 \times S^{D-2}$ where the spherical factor is the horizon. The holographic entanglement entropy of $AdS_2$ exactly reproduces the Schwarzschild black hole entropy which implies that black hole degrees of freedom live at asymptotic infinity. In generalized theories of gravity, the same procedure reproduces Wald entropy.
We introduce a new information-theoretic measure of multipartite quantum/classical correlations $Δ_P$, by generalizing the entanglement of purification to multipartite states. We provide proofs of its various properties, focusing on several entropic inequalities, in generic quantum systems. In particular, it turns out that the multipartite entanglement of purification gives an upper bound on multipartite mutual information, which is a generalization of quantum mutual information in the spirit of relative entropy. After that, motivated by a tensor network description of the AdS/CFT corresponden…
There are two proposals that compute holographic entanglement entropy in AdS$_3$ higher spin theories based on $SL(N,\mathbb{R})$ Chern-Simons theory. We show explicitly that these two proposals are equivalent. We also designed two methods that solve systematically the equations for arbitrary $N$. For finite charge backgrounds in AdS$_3$, we find exact agreement between our expressions and the short interval correction of the entanglement entropy for an excited state in a CFT$_2$.
The Ryu-Takayanagi conjecture provides a holographic description for the entanglement entropy for the strongly coupled holographic CFTs in the semi-classical limit. It proposes that the entanglement entropy is given by the area of the minimal homologous surface in the dual bulk. We show that the common terms of the entanglement entropy for the free massless fermions or bosons on a torus in the high-temperature expansion can be described by the sum of the signed area of extremal surfaces in the BTZ spacetime. The resulting EE and the corresponding bunch of the exgremal surfaces have preferable …
Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions. In the multipartite case we find the flows exhibit novel behavior which allows for a constrained flux on the boundary of the homology region. We show this flux can be made distinct from bipartite terms and reflects the truly multipartite portion of the holographic entanglement of purification.
We studied the holographic entanglement entropy for a strip and sharp wedge entangling regions in momentum relaxation systems. In the case of strips, we found analytic and numerical results for the entanglement entropy and showed the effect on the minimal surface by the electric field. We also studied the entanglement entropy of wedges and confirmed that there is a linear change in the electric field. This change is proportional to the thermoelectric conductivity, $\barα$, that can be measured.
We investigate holographically the entanglement entropy of a nonconformal medium whose dual geometry is described by an Einstein-Maxwell-dilaton theory. Due to an additional conserved charge corresponding to the number operator, its thermodynamics can be represented in a grandcanonical or canonical ensemble. We study thermodynamics in both ensembles by using the holographic renormalization and the entanglement entropy of a nonconformal medium. After defining the entanglement chemical potential which unlike the entanglement temperature has a nontrivial size dependence, we find that the entangle…
We present a five-dimensional fully anisotropic holographic model for heavy quarks supported by Einstein-dilaton-three-Maxwell action; one of the Maxwell fields is related to an external magnetic field. Influence of the external magnetic field on the 5-dim black hole solution and the confinement/deconfinement phase diagram is considered. The effect of the inverse magnetic catalyses is revealed and positions of critical end points are found.
In the presence of finite chemical potential $μ$, we holographically compute the entanglement of purification in a $2+1$- and $3+1$-dimensional field theory and also in a $3+1$-dimensional field theory with a critical point. We observe that compared to $2+1$- and $3+1$-dimensional field theories, the behavior of entanglement of purification near critical point is different and it is not a monotonic function of $\fracμ{T}$ where $T$ is the temperature of the field theory. Therefore, the entanglement of purification distinguishes the critical point in the field theory. We also discuss the depend…
