EVH Black Holes, AdS3 Throats and EVH/CFT Proposal

Within class of generic black holes there are extremal black holes (with vanishing Hawking temperature T) and vanishing horizon area Ah, but with finite Ah/T ratio,the Extremal Vanishing Horizon (EVH) black holes. We study the near horizon limit of a four dimensional EVH black hole solution to a generic (gauged) Einstein-Maxwell dilaton theory and show that in the near horizon limit they develop a throat which is a pinching orbifold limit of AdS3. This is an extension of the well known result for extremal black holes the near horizon limit of which contains an AdS2 throat. We show that in the near EVH near horizon limit the pinching AdS3 factor turns to a pinching BTZ black hole and that this near horizon limit is indeed a decoupling limit. We argue that the pinching AdS3 or BTZ orbifold is resolved if the near horizon limit is accompanied by taking the 4d Newton constant G4 to zero such that the Bekenstein-Hawking entropy S = Ah/(4G4) remains finite. We propose that in this limit the near horizon EVH black hole is dual to a 2d CFT. We provide pieces of evidence in support of the EVH/CFT correspondence and comment on its connection to the Kerr/CFT proposal and speculations how the EVH/CFT may be used to study generic e.g. Schwarzchild-type black holes.Comment: 31 pages, 3 figures, JHEP styl

Cardy and Kerr

The Kerr/CFT correspondence employs the Cardy formula to compute the entropy of the left moving CFT states. This computation, which correctly reproduces the Bekenstein--Hawking entropy of the four-dimensional extremal Kerr black hole, is performed in a regime where the temperature is of order unity rather than in a high-temperature regime. We show that the comparison of the entropy of the extreme Kerr black hole and the entropy in the CFT can be understood within the Cardy regime by considering a D0-D6 system with the same entropic properties.Comment: 20 pages; LaTeX; JHEP format; v.2 references added, v.3 Section 4 adde

A fixed point formula for the index of multi-centered N=2 black holes

We propose a formula for computing the (moduli-dependent) contribution of multi-centered solutions to the total BPS index in terms of the (moduli-independent) indices associated to single-centered solutions. The main tool in our analysis is the computation of the refined index Tr(-y)^{2J_3} of configurational degrees of freedom of multi-centered BPS black hole solutions in N=2 supergravity by localization methods. When the charges carried by the centers do not allow for scaling solutions (i.e. solutions where a subset of the centers can come arbitrarily close to each other), the phase space of classical BPS solutions is compact and the refined index localizes to a finite set of isolated fixed points under rotations, corresponding to collinear solutions. When the charges allow for scaling solutions, the phase space is non-compact but appears to admit a compactification with finite volume and additional non-isolated fixed points. We give a prescription for determining the contributions of these fixed submanifolds by means of a `minimal modification hypothesis', which we prove in the special case of dipole halo configurations.Comment: 61 pages, 3 figure

Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity

We study the conditions of marginal stability for two-center extremal black holes in N-extended supergravity in four dimensions, with particular emphasis on the N=8 case. This is achieved by exploiting triangle inequalities satisfied by matrix norms. Using different norms and relative bounds among them, we establish the existence of marginal stability and split attractor flows both for BPS and some non-BPS solutions. Our results are in agreement with previous analysis based on explicit construction of multi-center solutions.Comment: 1+15 pages; v2: some new formulas added and misprints corrected; v3: typos fixed, various refinements, Sec. 2.4 rewritten; to appear on JHE

The Heat Kernel on AdS_3 and its Applications

We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean) AdS_3 using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one loop partition function of N=1 supergravity on AdS_3. We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.Comment: 46 pages, LaTeX, v2: Reference adde

5d quivers and their AdS(6) duals

We consider an infinite class of 5d supersymmetric gauge theories involving products of symplectic and unitary groups that arise from D4-branes at orbifold singularities in Type I' string theory. The theories are argued to be dual to warped AdS(6)x S4/Zn backgrounds in massive Type IIA supergravity. In particular, this demonstrates the existence of supersymmetric 5d fixed points of quiver type. We analyze the spectrum of gauge fields and charged states in the supergravity dual, and find a precise agreement with the symmetries and charged operators in the quiver theories. We also comment on other brane objects in the supergravity dual and their interpretation in the field theories.Comment: 29 pages, 15 figure

On Symmetries of Extremal Black Holes with One and Two Centers

After a brief introduction to the Attractor Mechanism, we review the appearance of groups of type E7 as generalized electric-magnetic duality symmetries in locally supersymmetric theories of gravity, with particular emphasis on the symplectic structure of fluxes in the background of extremal black hole solutions, with one or two centers. In the latter case, the role of an "horizontal" symmetry SL(2,R) is elucidated by presenting a set of two-centered relations governing the structure of two-centered invariant polynomials.Comment: 1+13 pages, 2 Tables. Based on Lectures given by SF and AM at the School "Black Objects in Supergravity" (BOSS 2011), INFN - LNF, Rome, Italy, May 9-13 201

Kerr-CFT From Black-Hole Thermodynamics

We analyze the near-horizon limit of a general black hole with two commuting killing vector fields in the limit of zero temperature. We use black hole thermodynamics methods to relate asymptotic charges of the complete spacetime to those obtained in the near-horizon limit. We then show that some diffeomorphisms do alter asymptotic charges of the full spacetime, even though they are defined in the near horizon limit and, therefore, count black hole states. We show that these conditions are essentially the same as considered in the Kerr/CFT corresponcence. From the algebra constructed from these diffeomorphisms, one can extract its central charge and then obtain the black hole entropy by use of Cardy's formula.Comment: 19 pages, JHEP3, no figures. V2: References added, small typos fixe

Simple holographic duals to boundary CFTs

By relaxing the regularity conditions imposed in arXiv:1107.1722 on half-BPS solutions to six-dimensional Type~4b supergravity, we enlarge the space of solutions to include two new half-BPS configurations, which we refer to as the \kap\ and the \funnel. We give evidence that the \kap\ and \funnel\ can be interpreted as fully back-reacted brane solutions with respectively $AdS_2$ and $AdS_2\times S^2$ world volumes. \kap\ and \funnel\ solutions with a single asymptotic $AdS_3 \times S^3$ region are constructed analytically. We argue that \kap\ solutions provide simple examples of holographic duals to boundary CFTs in two dimensions and present calculations of their holographic boundary entropy to support the BCFT dual picture.Comment: 37 pages, pdflatex, 5 figure

Beyond Logarithmic Corrections to Cardy Formula

As shown by Cardy modular invariance of the partition function of a given unitary non-singular 2d CFT with left and right central charges c_L and c_R, implies that the density of states in a microcanonical ensemble, at excitations Delta and Delta-bar and in the saddle point approximation, is \rho_0(\Delta,\bar\Delta;c_L, c_R)=c_L c_R \exp(2\pi\sqrt{{c_L\Delta}/{6}})\exp(2\pi\sqrt{{c_R\bar\Delta}/{6}}). In this paper, we extend Cardy's analysis and show that in the saddle point approximation and up to contributions which are exponentially suppressed compared to the leading Cardy's result, the density of states takes the form \rho(\Delta,\bar\Delta; c_L,c_R)= f(c_L\Delta) f(c_R\bar\Delta)\rho_0(\Delta,\bar\Delta; c_L, c_R), for a function f(x) which we specify. In particular, we show that (i) \rho (\Delta,\bar\Delta; c_L, c_R) is the product of contributions of left and right movers and hence, to this approximation, the partition function of any modular invariant, non-singular unitary 2d CFT is holomorphically factorizable and (ii) \rho(\Delta,\bar\Delta; c_L, c_R)/(c_Lc_R) is only a function of $c_R\bar\Delta$ and $c_L\Delta$. In addition, treating \rho(\Delta,\bar\Delta; c_L, c_R) as the density of states of a microcanonical ensemble, we compute the entropy of the system in the canonical counterpart and show that the function f(x) is such that the canonical entropy, up to exponentially suppressed contributions, is simply given by the Cardy's result \ln\rho_0(\Delta,\bar\Delta; c_L, c_R).Comment: 30 pages, no figures; v2: minor improvements, one reference added, v3: minor corrections to match the published versio