The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the non-gravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the Einstein-Maxwell-scalar theory with topological terms in four and five dimensions and check that the above assumption was correct. Combining the computed central charge with the expected form of the temperature, the Bekenstein-Hawking entropy of the general extremal black holes in four and five dimensions can be reproduced by using the Cardy formula.
In this article, we review recent studies on multiple dual 2D CFT descriptions of the Kerr-Newman black hole, in terms of the Kerr/CFT and Reissner-Nordström/CFT correspondences. A microscopic hair conjecture is suggested.
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.
We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effe…
In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that two-dimensional and four-dimensional conformal anomalies (or corresponding central charges) have the same form as those obtained in AdS/CFT duality.
We discuss dilatonic gravity (bulk theory) from the point of view of (generalized) AdS/CFT correspondence. Self-consistent dilatonic background is considered. It may be understood as two boundaries space where AdS boundary appears as infinite boundary and new (singular) boundary occurs at short distances. The two-point correlation function and conformal dimension for minimal and dilaton coupled scalar are found. Even for minimal scalar, the conformal dimension is found to be different on above two boundaries. Hence, new CFT appears in AdS/CFT correspondence at short distances. AdS/CFT correspo…
We study real-time correlators in the Kerr/CFT correspondence. The near-horizon geometry of extreme and near-extremal Kerr black holes can be taken as warped spacetimes with the warping factors depending on the transverse radius and the angular variable. By considering the Kerr/CFT correspondence as a generalized warped AdS/CFT correspondence, we show how to compute the CFT real-time correlation functions. We find that the retarded Green's functions, the cross sections and the quasi-normal modes are all in perfect match with the predictions of the dual CFT. The same analysis is also generalize…
The prescription of the AdS/CFT correspondence is refined by using a regularization procedure, which makes is possible to calculate the divergent local terms in the CFT two-point function. We present the procedure for the example of the scalar field.
We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.
We show some implications of the approach to AdS/CFT correspondence based on Type IIB string in the flat space-time with D3-branes proposed in our previous paper. We discuss a correspondence for high energy scattering amplitudes of N=4 super-Yang-Mills proposed recently. We also discuss AdS/CFT correspondence at finite temperature. Our approach provides clear understanding of these issues.
By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.
We calculate the scalar quasinormal modes of warped $AdS_3$ black holes analytically. We find that in general they are not in agreement with the prediction of the usual AdS/CFT correspondence. Nevertheless, for the black hole not deviating far from BTZ black hole, the quasinormal frequencies are still well consistent with AdS/CFT correspondence.
We give a short introduction, beginning with the Kerr geometry itself, to the basic results, motivation, open problems and future directions of the Kerr/CFT correspondence.
Let $M$ be a complete Einstein manifold of negative curvature, and assume that (as in the AdS/CFT correspondence) it has a Penrose compactification with a conformal boundary $N$ of positive scalar curvature. We show that under these conditions, $H_n(M;Z)=0$ and in particular $N$ must be connected. These results resolve some puzzles concerning the AdS/CFT correspondence.
Using the AdS-CFT correspondence we calculate the two point function of CFT energy momentum tensors. The AdS gravitons are considered by explicitly solving the Dirichlet boundary value problem for $x_0=ε$. We consider this treatment as complementary to existing work, with which we make contact.
The occurence of 5d de Sitter space with 4d de Sitter brane is discussed on classical and quantum level. It is shown that quantum effects maybe produced by dual CFT living on the brane. Moreover, gravity trapping on the brane is proved via the presentation of 5d dS gravity as 4d gravity coupled with gauge theory. This supports the dS/CFT correspondence. Some open questions in 5d dS/4d CFT correspondence are briefly discussed.
We investigate the recently proposed Kerr/CFT correspondence in the context of rotating spacetimes with a NUT twist. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We try to understand the analog of singularities in the context of dual chiral CFT. Explicitly, we use Kerr/CFT correspondence to show that…
The dS/CFT correspondence differs from its AdS/CFT counterpart in some ways, yet is strikingly similar to it in many others. For example, both involve CFTs defined on connected spaces (despite the fact that the conformal boundary of deSitter space is not connected), and both impose constraints on scalar masses (Strominger's bound for deSitter, and the Breitenlohner-Freedman bound for Anti-deSitter). We argue that these similarities can be explored and exploited using a slight extension of the Euclidean approach to AdS/CFT. The methods are particularly compatible with Hull's embedding of deSitt…
We discuss how the variational principle can be used as a criterion for choosing, among scalar field actions implying the same equation of motion, the appropriate one for the AdS/CFT correspondence.
The loop expansion of the effective action is used to evaluate quantum corrections to a scalar field theory (massive phi^4 model) on AdS. We evaluate one loop corrections and show that they preserve conformal invariance of the boundary theory as conjectured by AdS/CFT correspondence.
We will study the AdS/CFT correspondence in an intermediate region between the strong form of this correspondence (string theory on AdS being dual to a boundary CFT), and the weak form of this correspondence (supergravity on AdS being dual to a boundary CFT). We will go beyond the supergravity approximation in the AdS by using the fact that strings have an extended structure. We will also calculate the CFT dual to such string corrections in the bulk, and demonstrate that they are consistent with the strong form of the AdS/CFT correspondence. So, even though the conformal dimensions of both the…
We extend the non-relativistic AdS/CFT correspondence to the fermionic fields. In particular we study the two point function of a fermionic operator in non-relativistic CFTs by making use of a massive fermion propagating in geometries with Schrodinger group isometry. Although the boundary of the geometries with Schrodinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in non-relativistic CFTs, thoug…
We calculate all components of thermal R-current correlators from AdS/CFT correspondence for non-zero momentum and energy. In zero momentum limit, we find an analytic expression for the components Gxx(Gyy). The dielectric function of strong coupling is also presented and compared with that in weak coupling.
We solve the Dirichlet boundary value problem for the massless gravitino on $AdS_{d+1}$ space and compute the two-point function of the dual CFT supersymmetry currents using the $AdS$/CFT correspondence principle. We find analogously to the spinor case that the boundary data for the massless $(d+1)$ dimensional bulk gravitino field consists of only a $(d-1)$ dimensional gravitino.
The gravitational energy is examined in asymptotically de Sitter space-times. The positivity will be shown for certain cases. The de Sitter/CFT(dS/CFT) correspondence recently proposed and cosmic no-hair conjecture are testified in the aspect of the gravitational energy. From the holographic renormalization group point of view, the two conjectures are deeply connected with each other.
In this paper, we use the appropriate boundary action for the vector fields near the horizon of near extremal Kerr black hole to calculate the two-point function for the vector fields in Kerr/CFT correspondence. We show the gauge-independent part of the two-point function is in agreement with what is expected from CFT.
We study the thermodynamics of the confined and unconfined phases of superconformal Yang-Mills in finite volume and at large N using the AdS/CFT correspondence. We discuss the necessary conditions for a smooth phase crossover and obtain an N-dependent curve for the phase boundary.
Logarithmic conformal field theory is investigated using the AdS/CFT correspondence and a novel method based on nilpotent weights. Using this device we add ghost fermions and point to a BRST invariance of the theory.
The AdS/CFT correspondence is established for the AdS_3 space compactified on a solid torus with the CFT field on the boundary. Correlation functions that correspond to the bulk theory at finite temperature are obtained in the regularization a'la Gubser, Klebanov, and Polyakov. The BTZ black hole solutions in AdS_3 are T-dual to the solution in the AdS_3 space without singularity.
Anomalies of N = (4,4) superconformal field theories coupled to a conformal supergravity background in two dimensions are computed by using the AdS/CFT correspondence. We find that Weyl, axial gauge and super Weyl transformations are anomalous, while general coordinate, local Lorentz, vector gauge and local super transformations are not. The coefficients of the anomalies show that the superconformal field theories have the central charge expected in the AdS/CFT correspondence.
We study the four--point function of chiral primaries corresponding to the dilaton--axion sector in supergravity in the $AdS_5$/CFT$_4$ correspondence. We find relations between some of the supergravity graphs and compute their leading singularities. We discuss the issue of logarithmic singularities and their significance for the OPE structure of the CFT.
In this article we review the recently discovered asymptotic integrability in the planar N = 4 SYM theory and discuss its breakdown beyond the asymptotic region due to the wrapping interactions. We also discuss novel dynamical tests of the AdS/CFT correspondence one can perform in the special cases when the wrapping interactions may be neglected.
We analyse the leading logarithmic singularities in direct and crossed channel limit of the four-point functions in dilaton-axion sector of type IIB supergravity on $AdS_{5}$ in AdS/CFT correspondence. Logarithms do not cancel in the full correlator in both channels.
We analyze the conformal invariance of submanifold observables associated with $k$-branes in the AdS/CFT correspondence. For odd $k$, the resulting observables are conformally invariant, and for even $k$, they transform with a conformal anomaly that is given by a local expression which we analyze in detail for $k=2$
Construction of a five dimensional conformal supergravity (D=5 CSG) is attempted by applying the AdS/CFT correspondence to the F(4) AdS supergravity in six dimensions. As a first step, local transformation laws of D=5 CSG have been established, from which the Weyl weights of the various fields in D=5 can be predicted.
We discuss a possible relation between singletons in $AdS$ space and logarithmic conformal field theories at the boundary of $AdS$. It is shown that the bulk Lagrangian for singleton field (singleton dipole) induces on the boundary the two-point correlation function for logarithmic pair. Bulk interpretation of mixing between logarithmic operator $D$ and zero mode operator $C$ under the scale transformation is discussed as well as some other issues.
We deform the AdS/CFT Correspondence by the inclusion of a non-supersymmetric scalar mass operator. We discuss the behaviour of the dual 5 dimensional supergravity field then lift the full solution to 10 dimensions. Brane probing the resulting background reveals a potential consistent with the operator we wished to insert.
We review recent progress in understanding the anti-de Sitter/conformal field theory correspondence in the context of two-dimensional dilaton gravity theory.
An improved correspondence formula is proposed for the calculation of correlation functions of a conformal field theory perturbed by multi-trace operators from the analysis of the dynamics of the dual field theory in Anti-de Sitter space. The formula reduces to the usual AdS/CFT correspondence formula in the case of single-trace perturbations.
This is a very brief review of some aspects of the AdS/CFT correspondence with an emphasis on the role of the topology of the boundary and the meaning of the sum over bulk geometries. To appear in the proceedings of the 73rd Meeting between Physicists and Mathematicians ``(A)dS/CFT correspondence,'' Strasbourg, September 11-13, 2003.
The requirement that the action be stationary for solutions of the Dirac equations in anti-de Sitter space with a definite asymptotic behaviour is shown to fix the boundary term (with its coefficient) that must be added to the standard Dirac action in the AdS/CFT correspondence for spinor fields.
We apply a recently proposed Kerr/CFT correspondence to extremal supersymmetric five-dimensional charged spinning black holes, constructed by Breckenridge, Myers, Peet and Vafa. By computing the central charge of the dual CFT and Frolov-Thorne temperature, Cardy's formula succeeds in reproducing Bekenstein-Hawking area law.
We investigate the slicing dependence of the relationship between conserved quantities in the (A)dS/CFT correspondence. Specifically, we show that the Casimir energy depends upon the topology and geometry of spacetime foliations of the bulk near the conformal boundary. We point out that the determination of the brane location in brane-world scenarios exhibits a similar slicing dependence, and we comment on this in the context of the AdS/CFT correspondence conjecture.
This paper presents a detailed discussion of the issue of supergravity perturbations around the flat five dimensional superspace required for manifest superspace formulations of the supergravity side of the AdS_{5}/CFT_{4} Correspondence.
We calculate the correction to the Bekenstein-Hawking entropy formula for five dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence. We then further generalise our analysis for the rotating black hole in five dimensional AdS space.
We study another realization of the Kerr/CFT correspondence. By imposing new asymptotic conditions for the near horizon geometry of Kerr black hole, an asymptotic symmetry which contains all of the exact isometries can be obtained. In particular, the Virasoro algebra can be realized as an enhancement of SL(2,R) symmetry of the AdS geometry. By using this asymptotic symmetry, we discuss finite temperature effects and show the correspondence concretely.
We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstrøm black hole in the viewpoint of the AdS$_2$/CFT$_1$ correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is $6 Q^2$ which is different from the previous result $6 Q^3$ of left moving sector obtained by warped AdS$_3$/CFT$_2$ description. We discussed the discrepancy in these two approaches and examined novel properties of our result.
In this paper we will study some aspects of dS/CFT correspondence. We will focus on the relation between Witten's non-standard de Sitter inner product and correlators in the holographic dual conformal field theory. We will argue that from the definition of Witten's inner product and conjecture that the Hilbert space of initial states of massive scalar field on $\mathcal{I}^-$ in de Sitter space corresponds to the Hilbert space of states of Euclidean CFT on $\mathcal{I}^-$, we can obtain CFT correlators in any vacuum state.
A survey of ideas, techniques and results from d=5 supergravity for the conformal and mass-perturbed phases of d=4 ${\cal N}$=4 Super-Yang-Mills theory
We construct a wave-functional whose argument couples to boundary fermion currents in the AdS/CFT correspondence. Using this we calculate the contributions from bulk fermions to the chiral anomaly that give the subleading order term in the exact $N$-dependence of the chiral anomaly of ${\cal N}=4$ SYM. The result agrees with the calculation of Bilal & Chu.
We discuss the entropy for the extremal BTZ black hole and the extremal EBTZ black hole. The EBTZ black hole means the BTZ black hole embedded in a five-dimensional(5D) black hole. The six-dimensional(6D) black string with traveling waves is introduced as a concrete model for realizing the AdS/CFT correspondence. The traveling waves carry the momentum distribution $p(u)$ which plays an important role in counting the entropy and establishing the correspondence. It turns out that the EBTZ black hole is consistent with the AdS/CFT correspondence.
We test the AdS/CFT correspondence in the case of a d=4 N=2 SCFT by comparing chiral anomalies which are of order N in the 't Hooft large N limit. These include corrections of order 1/N to the conformal anomaly, thus testing the correspondence beyond the extreme large N limit. The field theory anomalies are reproduced by terms in the 7-brane effective action in the bulk.
We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of $U(1)_Y$ symmetry for four-point functions.
The correspondence between the Kerr black hole and a boundary CFT has been conjectured recently. The conjecture has been proposed first only for the half of the CFT, namely for left movers. For right movers, the correspondence has been also found out through the suitable asymptotic boundary condition. However, the boundary conditions for these two studies are exclusive to each other. The boundary condition for left movers does not allow the symmetry of right movers, and vice versa. We propose new boundary condition which allows both of left and right movers.
The number of asymptotically de Sitter (non-singular) solutions of 5d dilatonic gravity with positive cosmological constant is found. These solutions are similar to the previously known asymptotically AdS spaces where dilaton may generate the singularity. Using these solutions the consistent $c$-function is proposed in the same way as in AdS/CFT. The consistency of RG flow gives further support for dS/CFT correspondence. From holographic RG flow equations we calculate the holographic 4d conformal anomaly with dilatonic contributions. This conformal anomaly turns out to be the same as in AdS/CF…
