In an odd-dimensional spacetime, gravity can be formulated as a proper gauge theory based on the Chern-Simons action for a suitable gauge group. Performing dimensional reduction, one obtains, as an effective theory, Chamseddine's even-dimensional topological gravity with the reduced gauge symmetry. This theory involves a multiplet of scalar fields that appear as a result of the dimensional reduction, and it is topological in the sense that its action does not depend on the metric. Focusing primarily on the four-dimensional case, we use the holographic dictionary to compute one-point correlation functions of the relevant boundary operators and find that the spin-current can have a nonzero expectation value in the dual quantum field theory. We also consider the generalized holographic Weyl anomaly and find that it vanishes. Finally, we propose a way of computing two-point correlation functions using the gravitational Wilson lines.
We consider holographic superconductors related to the Schwarzschild black hole in the low energy limit of Hořava-Lifshitz spacetime. The non-relativistic electromagnetic and scalar fields are introduced to construct a holographic superconductor model in Hořava-Lifshitz gravity and the results show that the $α_2$ term plays an important role, modifying the conductivity curve line by means of an attenuation the conductivity.
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…
We look into the $AdS$ black holes from two-dimensional gravity perspective. In this work, we extend the previous results of holographic renormalization group flows to dimensions two. By introducing a superpotential, we derive the flow equations in two-dimensional dilaton gravity. We find a quantity which monotonically decreases along flows and give some comments on holographic $c$-theorem. As examples, we show that recently studied supersymmetric $AdS$ black hole solutions generically dimensionally reduce to two-dimensional dilaton gravity, and obtain the flow equations for black hole solutio…
Massive gravity provides a holographic model for theories exhibiting momentum dissipation. We provide an analytic expression for the DC conductivity. The result is universal, depending only on properties of the infra-red horizon, and holds at finite temperature and charge density. In addition, we provide a derivation of black hole thermodynamics in holographic massive gravity and show that the resulting physics is sensible.
We study the holographic phase transition of superconductor dual to a Lifshitz black brane probed by an anisotropic scalar field in the probe limit in Hourava-Lifshitz gravity. With the use of numerical and analytical method, we investigate how the critical temperature of the condensation is affected by the Lifshitz exponent $z$, $α-$correction term in the action as well as the dimensions of the gravity. We also numerically explore the condensation of the dual operator and optical conductivity of the holographic system. Various interesting properties of the holographic condensation affected by…
We use the Chern-Simons formulation of higher spin theories in three dimensions to study aspects of holographic W-gravity. Concepts which were useful in studies of pure bulk gravity theories, such as the Fefferman-Graham gauge and the residual gauge transformations, which induce Weyl transformations in the boundary theory and their higher spin generalizations, are reformulated in the Chern-Simons language. Flat connections that correspond to conformal and lightcone gauges in the boundary theory are considered.
In this work, a clear connection is made between E. Verlinde's recent theory of emergent gravity in de Sitter space and the earlier work that described emergent gravity using holographic screens. A modified (non)holographic screen scenario is presented, wherein the screen fails to encode an emergent mass in the bulk "unemerged" part of space for sufficiently large length-scales, where the volume-law of the non-holographic bulk degrees of freedom overtakes the area-law scaling of the entropy of the screen. Within this framework, we can describe both an emergent dark gravitational force, which s…
We investigate the duality conjecture "Complexity=Action" (CA) for Born-Infeld (BI) gravity model and derive the growth rate of its action within the Wheeler-DeWitt (WDW) patch, which is believed to be dual to the growth rate of quantum complexity of holographic boundary state. In order to find the correct on-shell action, we use direct variational procedure to find proper boundary and corner terms. We find out that the late-time behavior of holographic complexity is the well-known two times of energy, as expected.
We argue that the holographic formula relating entanglement entropy and the area of a minimal surface is the key to define the area of surfaces in the (emergent) spacetime from the dual theory on the boundary. So we promote the entropy/area relation to operators to define the "area" observable in a holographic formulation of quantum gravity, then we find a suitable geometric representation for the states, and show that the Ryu-Takayanagi proposal is recovered in the approximation of semi-classical gravity. Finally, we discuss this picture in the example of a AdS-Black hole.
We revisit the late-time growth rate of various holographic complexity conjectures for neutral and charged AdS black holes with single or multiple horizons in two dimensional (2D) gravity like Jackiw-Teitelboim (JT) gravity and JT-like gravity. For complexity-action conjecture, we propose an alternative resolution to the vanishing growth rate at late-time for 2D neutral black hole with multiple horizons as found in the previous studies for JT gravity. For complexity-volume conjectures, we obtain the generic forms of late-time growth rates in the context of extremal volume and Wheeler-DeWitt vo…
I review recent work on holographic superconductivity with Einstein-Gauss-Bonnet gravity, and show how the critical temperature of the superconductor depends on both gravitational backreaction and the Gauss-Bonnet parameter, using both analytic and numerical arguments. I also review computations of the conductivity, finding the energy gap, and demonstrating that there is no universal gap ratio, $ω_g/T_c$, for these superconductors.
We construct a toy model for holographic superconductor with non linear Maxwell field in the frame of modified gravity. By probe the bulk background by non linear Maxwell fields we show that superconductivity happens under a specific critical temperature. The effect of the non linear Maxwell field and non linear curvature corrections have been studied by analytical matching methods. We conclude that the non linearity in Maxwell field and curvature coupling make condensation harder.
We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald's formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT's in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.
We compute the holographic stress tensor and the logarithmic energy-momentum tensor of Einstein-Weyl gravity at the critical point. This computation is carried out performing a holographic expansion in a bulk action supplemented by the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined by the addition of this topological term has the remarkable feature that all Einstein modes are identically cancelled both from the action and its variation. Thus, what remains comes from a nonvanishing Bach tensor, which accounts for non-Einstein modes associated to logarithmic terms wh…
We study certain features of a strongly coupled theory whose gravitational dual is given by two-charge dilatonic black hole in AdS5 which has recently been used to study holographic Fermi liquids. By making use of the gravity description, we have studied conductivity, holographic entanglement entropy and dynamics of a charged scalar field. In particular at low energy we find that the temperature dependence of the real part of the conductivity goes as T^3 and the background is stable against scalar condensations.
We consider universal aspects of a holographic Schwinger effect in general backgrounds with an external homogeneous electric field. The argument is based on the potential analysis developed in our previous work. Under some conditions, there always exists a critical electric field, above which the potential barrier vanishes and the system becomes unstable catastrophically. The critical value agrees with the one obtained from the Dirac-Born-Infeld action. For general confining backgrounds, we show that the Schwinger effect does not occur when the electric field is weaker than the confining strin…
We construct a holographic p-wave superconductor model in the framework of quasi-topological gravity in the probe limit. The relation between the critical temperature and the coupling parameters of higher curvature terms is investigated. The numerical results for conductivity are presented as well. It turns out that our data fits the Drude model very well in the low frequency limit, and the values of DC conductivity as well as the relaxation time are obtained numerically.
We investigate numerically $f(R)$ gravity effects on certain AdS/CFT tools including holographic entanglement entropy and two-point correlation functions for a charged single accelerated Anti-de Sitter black hole in four dimensions. We find that both holographic entanglement entropy and two-point correlation functions decrease by increasing acceleration parameter $A$, matching perfectly with literature. Taking into account the $f(R)$ gravity parameter $η$, the decreasing scheme of the holographic quantities persist. However, we observe a transition-like point where the behavior of the holograp…
We use the holographic language to show the existence of the $a$-theorem for even dimensional CFTs, dual to the AdS space in general quadratic curvature gravity. We find the Wess-Zumino action which is originated from the spontaneous breaking of the conformal symmetry in $d\leq 8$, by using a radial cut-off near the AdS boundary. We also study the RG flow and (average) null energy condition in the space of the couplings of theory. In a simple toy model, we find the regions where this holographic RG flow has a monotonic decreasing behavior.
Naively applying holographic duality to gapped gravity on Anti de Sitter (AdS) space seems to suggest that the stress tensor of the field theory dual cannot be conserved. On the other hand, by symmetry arguments, it seems that the dual should not violate Poincare symmetry. To clarify this apparent contradiction, we study a holographic dual of massive gravity where both the physical background metric and the fiducial metric are AdS. Using the anomalous scaling of the energy momentum tensor as our guide, we conclude that the dual theory is nonlocal. We find that the dual is similar to conformal …
We obtain holographically renormalized boundary stress tensors with the emphasis on a special point in the parameter space of three dimensional new massive gravity, using the so-called Fefferman-Graham coordinates with relevant counter terms. Through the linearized equations of motion with a standard prescription, we also obtain correlators among these stress tensors. We argue that the self-consistency of holographic renormalization determines counter terms up to unphysical ambiguities. Using these renormalized stress tensors in Fefferman-Graham coordinates, we obtain the central charges of du…
In this paper we study the application of holographic entanglement negativity proposal for bipartite states in the 2d Galilean conformal field theory ($GCFT_2$) dual to bulk asymptotically flat spacetimes in the context of generalized minimal massive gravity (GMMG) model. $GCFT_2$ is considered on the boundary side of the duality and the bulk gravity is described by GMMG that is asymptotically symmetric under the Galilean conformal transformations. In this paper, the replica technique, based on the two-point and the four-point twist correlators, is utilized and the entanglement entropy and the…
This thesis reviews the conjectured holographic relation between entanglement and gravity due to Mark van Raamsdonk and collaborators. It is accounted how the linearized Einstein equations both with and without matter in a d+1-dimensional AdS background can be derived from the first law of entanglement entropy in a d-dimensional CFT. This derivation builds on the Ryu-Takayanagi formula that relates entanglement entropy for CFT subsystems to extremal surfaces in the AdS bulk. The relation between gravity and entanglement is also corroborated by a qualitative investigation of the duality between…
We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic non-conformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force…
In AdS/CFT, the holographic Weyl anomaly computation relates the a-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility of a holographic c-theorem for the a-anomaly under flows to the IR. We prove such a c-theorem for higher curvature Lovelock gravity, where the bulk equations of motion remain second order. We also explore f(R) gravity as a toy model where higher derivatives cannot be avoided. In this case, monoticity of the flow requires an additional condition related to the higher derivative nature of the theory. Th…
We study holographic renormalization for three dimensional new massive gravity (NMG). By studying the general fall off conditions for the metric allowed by the model at infinity, we show that at the critical point where the central charges of the dual CFT are zero it contains a leading logarithmic behavior. In the context of AdS/CFT correspondence it can be identified as a source for an irrelevant operator in the dual CFT. The presence of the logarithmic fall off may be interpreted as the fact that the dual CFT would be a LCFT.
We study the Hawking-Page transition in a holographic model of field theories with momentum dissipation. We find that the deconfinement temperature strictly decreases as momentum dissipation is increased. For sufficiently strong momentum dissipation, the critical temperature goes to zero, indicating a zero-temperature deconfinement transition in the dual field theory.
The asymptotic behavior of new massive gravity (NMG) is analyzed for all values of the mass parameter satisfying the Breitenlohner-Freedman bound. The traditional Fefferman-Graham expansion fails to capture the dynamics of NMG, and new terms in the asymptotic expansion are needed to include the massive graviton modes. New boundary conditions are discovered for a range of values $-1<2m^2l^2<1$ at which non-Einstein modes decay more slowly than the Brown-Henneaux boundary conditions. The holographically renormalized stress tensor is computed for these modes, and the relevant counterterms are ide…
We use the variational method for the Sturm-Liouville eigenvalue problem to analytically calculate some properties of holographic superconductors with Gauss-Bonnet gravity in probe limit. By studying the holographic p-wave and s-wave superconductors in (3+1)-dimensional boundary field theories, it is found that near the critical temperature, the critical exponent of the condensation is 1/2 which is the universal value in mean-field theory. We also find that when Gauss-Bonnet coefficients grow bigger the operators on the boundary field theory will be harder to condense. These are in good agreem…
In this paper we review some results on the generalization of the gauge/gravity duality to include fundamental matter by means of probe branes. We compute the meson spectrum of maximally supersymmetric gauge theories in several dimensions, both in the Coulomb and Higgs branch. We also study the addition of flavor and compute the meson spectrum for non-commutative theories. Additionally, we present a thorough search of supersymmetric embeddings of probe branes in the Klebanov-Witten model.
We consider the effects of momentum relaxation on the topological quantum phase transitions in holographic Weyl semimetals. The translational symmetry breaking in the field theory is realized in the framework of massive gravity. We find that the critical value of the phase transition, characterized by the anomalous Hall conductivity, decreases with the increasing of graviton mass, i.e. the momentum relaxation strength. There exists a critical value of graviton mass above which the topological phase transition disappears and therefore the Weyl points are destroyed. All these phenomena are quali…
We holographically compute the Rényi relative divergence $D_α (ρ_{+} || ρ_{-})$ between two density matrices $ρ_{+}, \; ρ_{-}$ prepared by path integrals with constant background fields $λ_{\pm}$ coupled to a marginal operator in JT gravity. Our calculation is non perturbative in the difference between two sources $ λ_{+} -λ_{-}$. When this difference is large, the bulk geometry becomes a black hole with the maximal temperature allowed by the Rényi index $α$. In this limit, we find an analytic expression of the Rényi relative divergence, which is given by the on shell action of the back reacte…
We consider non-linear massive gravity with two Stückelberg fields in which the diffeomorphism invariance is broken spontaneously in two of the spacetime directions. This theory admits a charged anti-de Sitter black brane solution and has recently been used in holographic context as a bulk description of a boundary field theory with momentum dissipation. Here we study the stability of the black brane solution. We identify the physical degrees of freedom and determine the healthy regions of the parameter space of the theory. We find that there is a region in parameter space, where the theory su…
We establish the gravity/fluid correspondence in the nonminimally coupled scalar-tensor theory of gravity. Imposing Petrov-like boundary conditions over the gravitational field, we find that, for a certain class of background metrics, the boundary fluctuations obey the standard Navier-Stokes equation for an incompressible fluid without any external force term in the leading order approximation under the near horizon expansion. That is to say, the scalar field fluctuations does not contribute in the leading order approximation regardless of what kind of boundary condition we impose on it.
In this paper we suggest a connection between quantum mechanics and Verlinde's recently proposed entropic force theory for the laws of Newton. We propose an entropy based on the quantum mechanical probability density distribution. With the assumption that the holographic principle holds we propose that our suggested quantum entropy generalizes the Bekenstein entropy used by Verlinde in his approach. Based on this assumption we suggest that Verlinde's entropic theory of gravity has a quantum mechanical origin. We establish a reformulation of the Newtonian potential for gravity based on this qua…
In this work, the s-wave, p-wave and d-wave holographic superconductors in the Hořava-Lifshitz gravity are investigated in the probe limit. For the present approach, it is shown that the equations of motion for different wave states in Einstein gravity can be written into a unified form, and condensates take place in all three cases. This scheme is then generalized to Hořava-Lifshitz gravity, and an unified equation for multiple holographic states is obtained. Furthermore, the properties of the condensation and the optical conductivity are studied numerically. It is found that, in the case of …
We construct a new toy model of the holographic principle, named as holographic qubit threads model, which is an enlightening step towards the issue of spacetime emergence ("it from qubit"). More specifically, we propose for the first time that each bit thread in a locking bit thread configuration is in a "qubit" state, i.e., the quantum superposition state of two orthogonal states. Using this thread/state correspondence, we can construct the explicit expressions for the SS states corresponding to a set of bulk extremal surfaces in the surface/state correspondence, and nicely characterize thei…
We perform a detailed analysis of holographic entanglement Rényi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the Rényi entropy as well as the scaling dimension of the twist operators in the dual field theory. Consistency of these results are verified from the AdS/CFT correspondence, via a corresponding computation of the Weyl anomaly on the gravity side. Similar analyses are then carried out for thre…
In this paper, the holographic p-wave superfluid model with charged complex vector field is studied in dRGT massive gravity beyond the probe limit. The stability of p-wave and p+ip solutions are compared in the grand canonical ensemble. The p-wave solution always get lower value of grand potential than the p+ip solution, showing that the holographic system still favors an anisotropic (p-wave) solution even with considering a massive gravity theory in bulk. In the holographic superconductor models with dRGT massive gravity in bulk, a key sailing symmetry is found to be violated by fixing the re…
We introduce the gauge/gravity, or AdS/CFT, correspondence with an eye towards its application to strongly coupled systems. We provide an overview of the duality, including the AdS/CFT dictionary and holographic renormalization. We then discuss simple correlation functions in the context of renormalization group flow geometries, holographic thermodynamics and an application to the phase diagram of QCD, real-time correlators and the shear viscosity of strongly coupled field theories, holographic superconductors, and the application of holographic fermionic response to strange metals. These lect…
Recent progress in the holographic approach makes it more transparent that each conductivity can be decomposed into the coherent contribution due to momentum relaxation and the incoherent contribution due to intrinsic current relaxation. In this paper we investigate this decomposition in the framework of Einstein-Maxwell-dilaton theory. We derive the perturbation equations, which are decoupled for a large class of background solutions, and then obtain the analytic results of conductivity with the slow momentum relaxation in low frequency approximation, which is consistent with the known result…
We compute holographic Rényi entropies for spherical entangling surfaces on the boundary while considering third order Lovelock gravity with negative cosmological constant in the bulk. Our study shows that third order Lovelock black holes with hyperbolic event horizon are unstable, and at low temperatures those with smaller mass are favoured, giving rise to first order phase transitions in the bulk. We determine regions in the Lovelock parameter space in arbitrary dimensions, where bulk phase transitions happen and where boundary causality constraints are met. We show that each of these points…
We study holographic entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling $λ_{GB}$. We show that for $λ_{GB} > 0$ the holographic entanglement entropy probe explores less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for $λ_{G…
We study the entanglement wedge cross-section (EWCS) in holographic massive gravity theory, in which a first and second-order phase transition can occur. We find that the mixed state entanglement measures, the EWCS and mutual information (MI) can characterize the phase transitions. The EWCS and MI show exactly the opposite behavior in the critical region, which suggests that the EWCS captures distinct degrees of freedom from that of the MI. More importantly, EWCS, MI and HEE all show the same scaling behavior in the critical region. We give an analytical understanding of this phenomenon. By co…
In the paper using matching method in the probe limit, we investigate some properties of holographic superconductor in Gauss-Bonnet gravity with Born-Infeld electrodynamics . We discuss the effects of the Gauss-Bonnet coupling $\a$ and Born-Infeld parameter $b$ on the critical temperature and condensate. We find that both of $\a$ and $b$ make the critical temperature decrease, which implies the condensate harder to form. Moreover we study the magnetic effect on holographic superconductor and obtain that the ratio between the critical magnetic field and the square of the critical temperature in…
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.
