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 solutions.
Holographic Renormalization Group (RG) in nine dimensions is considered. The d8 holographic conformal anomaly is found. It should correspond to d8 CFT in AdS_9/CFT_8 correspondence. The comparison of holographic and QFT anomalies in d8 de Sitter space is done. It may give the indication for rigorous AdS_9/CFT_8 correspondence proposal.
The equivalence between the holographic renormalization group and the soft dilaton theorem is shown for a class of wrapped metrics solutions of the string beta function equations for the bosonic string.
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…
In this lecture, we review the derivation of the holographic renormalization group given in hep-th/9912012. Some extra background material is included, and various applications are discussed.
It is shown that the Holographic Renormalization Group can be formulated universally within Quantum Field Theory as (the quantization of) the Hamiltonian flow on the cotangent bundle to the space of gauge-invariant single-trace operators supplied with the canonical symplectic structure. The classical Hamiltonian dynamics is recovered in the large $N$ limit.
Notes on holographic renormalization as a tool for UV analysis and derivation of the two-point Ward identity encoding symmetry breaking. Goldstone theorem is reviewed, discussing in particular the modifications required by its extension to non-relativistic field theories. The Ward identity encoding both spontaneous and explicit breaking are derived by general principles. Holographic renormalization is presented in a quite operational fashion. The derivation of the Ward identity in holography is illustrated by an example.
We derive the four-point correlators of scalar operators of dimension one in the supergravity limit of the D1D5 CFT holographically dual to string theory on AdS$_3\times S^3\times \mathcal{M}$, with $\mathcal{M}$ either $T^4$ or $K3$. We avoid the use of Witten diagrams but deduce our result from a limit of the heavy-heavy-light-light correlators computed in arXiv:1705.09250, together with several consistency requirements of the OPE in the various channels. This result represents the first holographic correlators of single-trace operators computed in AdS$_3$.
In this Letter, we consider a Non-Commutative (NC) extension of AdS-CFT correspondence and its effects on holographic superconductors. NC corrections are incorporated via the NC generalization of Schwarzschild black hole metric in AdS with the probe limit. We study NC effects on the relations connecting the charge density and the critical temperature of the Holographic Superconductors. Furthermore, condensation operator of the superconductor has been analyzed. Our results suggest that generically, NC effects increase the critical temperature of the holographic superconductor.
The bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the $\mathcal{N}=4$ super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its $SL(2,\mathbf{Z})…
We calculate the holographic conformal anomaly and brane Newton potential when bulk is 5d AdS BH. It is shown that such anomaly is the same as in the case of pure AdS or (asymptotically) dS bulk spaces, i.e. it is (bulk) metric independent one. While Newton potential on the static brane in AdS BH is different from the one in pure AdS space, the gravity trapping still occurs for two branes system. This indicates to metric independence of gravity localization.
We review holographic renormalization for non-conformal branes using the Hamilton-Jacobi formalism. We provide the tools required for the computation of the holographic dictionary, while we present some marginally new technical results regarding holographic renormalization for $Dp$-branes, $p<5$, for Einstein-Maxwell theory coupled to a dilaton. The computations are based on a recursive algorithm by Papadimitriou, that solves the radial Hamilton-Jacobi equation in the asymptotic boundary of the bulk. This paper is a short version of the Master thesis of the author written in 2014 at the Instit…
We establish our recently proposed holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with concrete higher dimensional examples. In this context we compute the holographic entanglement negativity for mixed states of adjacent subsystems in $d$-dimensional conformal field theories dual to bulk $AdS_{d+1}$ vacuum and $AdS_{d+1}$-Schwarzschild black holes. These representative examples provide strong indication for the universality of our conjecture which affirms significant implications for diverse applications.
We show that in general holographic stress tensor may contain a new term of divergence of a spacelike unit normal acceleration. Then, it is shown that in contrast to previous descriptions, a new stress tensor for Kerr-AdS solutions can be a traceless one. Interestingly, this prescription entails a local failure on the IR-UV connection.
Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. Using this formalism, we independently replicate the holographic RG flow narrative to go on to …
Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The formula is checked for some simple examples from the AdS/CFT correspondence, but can be applied also in non-AdS/non-CFT cases.
We study the Crofton's formula in the Lorentzian AdS$_3$ and find that the area of a generic space-like two dimensional surface is given by the flux of space-like geodesics. The "complexity=volume" conjecture then implies a new holographic representation of the complexity in terms of the number of geodesics. Finally, we explore the possible explanation of this result from the standpoint of information theory.
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 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 develop parallels between the holographic renormalization group in the bulk and the Wilsonian renormalization group in the dual field theory. Our philosophy differs from most previous work on the holographic RG; the most notable feature is the key role of multi-trace operators. We work out the forms of various single- and double-trace flows. The key question, `what cutoff on the field theory corresponds to a radial cutoff in the bulk?' is left unanswered, but by sharpening the analogy between the two sides we identify possible directions.
We perform holographic renormalization for probe branes in AdS_5 x S^5. We show that for four known probe D-branes wrapping an AdS_m x S^n, the counterterms needed to render the action finite are identical to those for the free, massive scalar in AdS_m plus counterterms for the renormalization of the volume of AdS_m. The four cases we consider are the probe D7, two different probe D5's and a probe D3. In the D7 case there are scheme-dependent finite counterterms that can be fixed by supersymmetry.
We discuss Holographic Renormalization Group equations in the presence of fermions and form fields in the bulk. The existence of a holographically dual quantum field theory for a given bulk gravity theory imposes consistency conditions on the ranks of the form fields, the fermion - form field couplings, and leads to a novel Ward identity.
The problem of finding a holographic CFT dual to string theory on AdS(3)xS(3)xS(3)xS(1) is examined in depth. This background supports a large N=4 superconformal symmetry. While in some respects similar to the familiar small N=4 systems on AdS(3)xS(3)xK3 and AdS(3)xS(3)xT4, there are important qualitative differences. Using an analog of the elliptic genus for large N=4 theories we rule out all extant proposals -- in their simplest form -- for a holographic duality to supergravity at generic values of the background fluxes. Modifications of these extant proposals and other possible duals are di…
We construct a three-dimensional geometry interpolating two different AdS spaces. From the dual quantum field theory viewpoint, it corresponds to a nontrivial renormalization group flow from a UV to another IR conformal field theory. On this geometry, we discuss the change of the central charge in a momentum-space and real-space renormalization group flow. The result shows in both renormalization prescriptions that the central charge monotonically decreases along the renormalization group flow.
We perform the potential analysis for the holographic Schwinger effect in a deformed $AdS_5$ model with conformal invariance broken by a background dilaton. We evaluate the static potential by analyzing the classical action of a string attaching the rectangular Wilson loop on a probe D3 brane sitting at an intermediate position in the bulk AdS space. We observe that the inclusion of chemical potential tends to enhance the production rate, reverse to the effect of confining scale. Also, we calculate the critical electric field by Dirac-Born-Infeld (DBI) action.
Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.
Stability of dilatonic AdS spaces due to quantum effects of dilaton coupled conformal matter is considered. When such spaces do not exist on classical level, their dynamical generation occurs. Explicit examples corresponding to quantum creation of d4 dilatonic AdS Universe and of d2 dilatonic AdS Black Hole (BH) are presented. Motivated by holographic RG, in the similar approach the complete d5 effective action is discussed. The intermediate region where it is the sum of two parts: bulk (classical gravity) and boundary quantum action is investigated. The effective equations solution representi…
We have studied holographic Wilsonian renormalization group (HWRG) of free massless fermionic fields in AdS space and its stochastic quantization(SQ) by identifying the Euclidean action with its boundary on-shell action. The natural extension of the relation between stochastic 2-point correlation function and double trace coupling obtained from HWRG computation conjectured in arXiv:1209.2242 to fermionic fields is established. We have confirmed that the stochastic 2-point function precisely captures the radial flow of the double trace coupling via this relation.
We consider Toda field theories in a classical Euclidean $AdS_2$ background. We compute the four-point functions of boundary operators in the $a_1$, $a_2$ and $b_2$ Toda field theories. They take the same form as the four-point functions of generators in the corresponding $\mathcal{W}$-algebras. Therefore we conjecture that the boundary operators are in one-to-one correspondence with the generators in the $\mathcal{W}$-algebras.
We propose a covariant holographic entanglement negativity constructionfor time-dependent mixed states of adjacent intervals in $(1+1)$-dimensional conformal field theories dual to non-static bulk $\mathrm{AdS_3}$ configurations. Our construction applied to $(1+1)$-dimensional conformal field theories with a conserved charge dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the corresponding replica technique results, in the large central charge limit. We also utilize our conjecture to obtain the time-dependent holographic entanglement negativity for the mixed state…
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 investigate the structure of holographic renormalization in the presence of sources for irrelevant operators. By working perturbatively in the sources we avoid issues related to the non-renormalizability of the dual field theory. We find new classes of divergences which appear to be non-local on the gravity side. However in all cases a systematic renormalization procedure exists involving either standard local counterterms or new counterterms which may be interpreted as multi-trace counterterms in the field theory. The multi-trace counterterms reflect a more intricate relation between sourc…
We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic ren…
We explicitly obtain energy-momentum tensor at the asymptotic 3-dimensional region of Schwarzschild AdS$_4$ and Taub-NUT-(A)dS$_4$ using the so-called `counter-term subtraction method' in Fefferman-Graham coordinate. The energy momentum tensor is presented in a closed form for the AdS$_4$ and for the special case of Taub-NUT-dS and in an asymptotic series for other cases. The result suggests that in light of AdS/CFT correspondence, the 3-dimensional trace anomaly can be expressed in terms of the 3-dimensional volume and Ricci scalar.
We extend the relation between stochstic quantization and Holographic Wilsonian Renormalization Group to the massive fermion case in Euclidean AdS space. The original suggestion about the explicit relation between the two theories is in arXiv:1209.2242. To give a fermion bulk action the Dirichlet boundary condition and the Neumann boundary condition, there are some additional terms to the bulk action. We have confirmed that the relation also hold for massive fermion case.
We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) dual to bulk non static $AdS_3$ geometries. Application of our proposal to such mixed states in a $CFT_{1+1}$ dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a $CFT_{1+1}$ dual to a bulk Vaidya-$AdS_3$ ge…
We discuss marginal deformations of warped AdS$_3\times$S$^2$ solutions preserving small $\mathcal{N}=(0,4)$ supersymmetry in massive IIA and eleven-dimensional supergravity and obtain a whole family of new solutions. We characterise these new backgrounds by studying some observables like the quantised charges, associated Hannany-Witten brane set-ups and the holographic central charge, the latter is shown to be invariant under the deformation. The study of the preservation of supersymmetry shows that the new backgrounds support an identity structure on the internal five-dimensional space, whic…
We construct the two dimensional N=(0,4) gauge theory that lives on the world volume of D1-branes and intersecting D5-branes. We conjecture that this theory flows in the infra-red to a fixed point with large N=(4,4) superconformal symmetry. The central charge of the conformal field theory is shown to coincide with the holographic dual of string theory compactified on AdS3 x S3 x S3 x S1.
We consider the 5d Kerr-AdS black hole as a gravity dual to rotating quark-gluon plasma. In the holographic prescription we calculate the drag force acting on a heavy quark. According to the holographic approach a heavy quark can be considered through the string in the gravity dual. We study the dynamics of the string for the Kerr-AdS backgrounds with one non-zero rotational parameter and two non-zero rotational parameters that are equal in magnitude. For the case of one non-zero rotational parameter we find good agreement with the prediction from the 4d case considered by arXiv:1012.3800).
We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T \bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be…
In this paper, we consider AdS$_3$ with Comp$\grave{\mathrm{e}}$re-Song-Strominger (CSS) boundary conditions, under which the dual field theory is warped conformal field theory (WCFT), featuring a Virasoro-Kac-Moody algebra. We provide a holographic dual picture of the single interval entanglement entropy in WCFT in the bulk AdS$_3$. We explicitly show that the bulk object captures the entanglement entropy in WCFT is a massive spinning particle's worldline that anchored on the boundary of the interval. Given the mass and spin of the particle as functions of quantum numbers of the twist operato…
The gauge theory dual to the decay of an unstable D-particle in AdS is analysed in terms of coherent states. We discuss in detail how to count the number of particles in the decay product. We find, in agreement with the analysis in flat space, that the emission amplitude is suppressed as the mass of the radiated particles increases.
We give a prescription for calculating the holographic Weyl anomaly in arbitrary dimension within the framework based on the Hamilton-Jacobi equation proposed by de Boer, Verlinde and Verlinde. A few sample calculations are made and shown to reproduce the results that are obtained to this time with a different method. We further discuss continuum limits, and argue that the holographic renormalization group may describe the renormalized trajectory in the parameter space. We also clarify the relationship of the present formalism to the analysis carried out by Henningson and Skenderis.
We investigate subregion holographic complexity in the context of renormalization group flow geometries. We use both the Poincaŕe slicing and the Janus ansatz as holographic duals to renormalization group flows in the boundary conformal field theory. In the former metric, subregion complexity is computed for a disc and a strip shaped entangling region. For the disc shaped region, consistent emergence of length scales for flow to the deep infra-red is established. For strip shaped regions, we find that complexity cannot locate holographic phase transitions in a sharp domain wall scenario. For s…
Based on the context of complexity = action (CA) conjecture, we calculate the holographic complexity of AdS black holes with planar and spherical topologies in Horndeski theory. We find that the rate of change of holographic complexity for neutral AdS black holes saturates the Lloyd's bound. For charged black holes, we find that there exists only one horizon and thus the corresponding holographic complexity can't be expressed as the difference of some thermodynamical potential between two horizons as that of Reissner-Nordstrom AdS black hole in Einstein-Maxwell theory. However, the Lloyd's bou…
In this paper, we consider a deformed AdS background and study effect of deformation parameter on the pair production rate of the Schwinger effect. The electrostatic potential is important for the pair production in the holographic Schwinger effect. In this paper, we analyze the electrostatic potential in a deformed AdS background and investigate the effect of deformation parameter which may be useful to test of AdS/QCD. In the case of zero temperature we find that larger value of the deformation parameter leads to a smaller value of separation length of the test particles on the probe. Also w…
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$…
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, of holographic Ward identities, anomalies and RG equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holograp…
We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) through the $AdS_3/CFT_2$ correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $CFT_{1+1}$. The construction is utilized to compute the holographic entanglement negativity for such mixed states i…
We investigate the holographic description of a superconductor constructed in the (2+1)-dimensional AdS soliton background in the probe limit. We study the holographic properties through both analytical and numerical methods. With analytical methods, we are the first to obtain the exact formula for critical phase transition points as $μ_{c}=1+\sqrt{1+m^2}$. Around the transition points, we find a correspondence between the value of the scalar field at the tip and the scalar operator at infinity. We also generalize the front properties to holographic models in higher dimensional AdS soliton spa…
We determine the boundary terms of the free higher-spin action which reproduce the AdS Fronsdal equations in an AdS manifold with a finite distance boundary. The boundary terms are further constrained by the gauge invariance of the total action. We show that, for spins larger than two, no local boundary term can restore the full gauge symmetry, and the broken symmetry corresponds to higher-spin Weyl transformations on the boundary CFT. The boundary action is used for the evaluation of the on-shell higher-spin AdS action in terms of the boundary data given by a conformal higher-spin field.
Holographic model of massive scalar field with its self-interaction $λϕ^n$ in AdS space is able to give a logarithmic scale dependence to marginal multi trace deformation couplings on its dual conformal field theory, where $λ$ is the self-interaction coupling of the scalar field, $ϕ$ and $n$ is an integral number. In arXiv:1501.06664, the authors realize this feature by looking at bulk scalar solutions near AdS boundary imposing a specific boundary condition between the coefficients of non-normalizable and normalizable modes of the scalar field excitations. We study the same holographic model …
Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if …
A heavy quark moving through a strongly coupled deconfined plasma has a holographic dual description as a string moving in a black brane geometry. We apply the holographic Wilsonian renormalization method to derive a holographic effective string action dual to the heavy quark. The effective action only depends on the geometry between the black brane horizon and a cutoff localized in the radial direction, corresponding to the IR of the dual theory. We derive RG flow equations for the coefficients in the effective action and show that the force acting on the heavy quark is independent of the pos…
We substantiate a covariant proposal for the holographic reflected entropy in $CFT$s dual to non-static $AdS$ geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the $AdS_3/CFT_2$ scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in $CFT_{1+1}$s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for t…
We consider the holographic duality for a generic bulk theory of scalars coupled to gravity. By studying the fluctuations around Poincare invariant backgrounds with non-vanishing scalars, with the scalar and metric boundary conditions considered as being independent, we obtain all one- and two-point functions in the dual renormalization group flows of the boundary field theory. Operator and vev flows are explicitly distinguished by means of the physical condensates. The method is applied to the GPPZ and Coulomb branch flows, and field theoretical expectations are confirmed.
In earlier work the evolution operator for the exact RG equation was mapped to a field theory in Euclidean AdS. This gives a simple way of understanding AdS/CFT. We explore aspects of this map by studying a simple example of a Schroedinger equation for a free particle with time dependent mass. This is an analytic continuation of an ERG like equation. We show for instance that it can be mapped to a harmonic oscillator. We show that the same techniques can lead to an understanding of dS/CFT too.
