Do supersymmetric anti-de Sitter black rings exist?

We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conical singularity, which suggests that nonsupersymmetric anti-de Sitter black rings may exist but cannot be "balanced" in the supersymmetric limit.Comment: Latex, 18 pages, 1 figure. v2: minor change

Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT

Using the general framework developed in hep-th/0607056, we study in detail the phase space of BPS Black Holes in AdS, for the case where all three electric charges are equal. Although these solitons are supersymmetric with zero Hawking temperature, it turns out that these Black Holes have rich phase structure with sharp phase transitions associated to a corresponding critical generalized temperature. We are able to rewrite the gravity variables in terms of dual CFT variables and compare the gravity phase diagram with the free dual CFT phase diagram. In particular, the elusive supergravity constraint characteristic of these Black Holes is particulary simple and in fact appears naturally in the dual CFT in the definition of the BPS Index. Armed with this constraint, we find perfect match between BH and free CFT charges up to expected constant factors.Comment: 14 pages, 5 figures, corrected typos and references adde

A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes

We identify a large family of 1/16 BPS operators in N=4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS_5 black holes when the main contribution to their masses is given by their angular momentum.Comment: 32 pages, 6 figures, LaTeX uses JHEP3 class; ver 2- added acknowledgment, minor change

On a class of 4D Kahler bases and AdS_5 supersymmetric Black Holes

We construct a class of toric Kahler manifolds, M_4, of real dimension four, a subset of which corresponds to the Kahler bases of all known 5D asymptotically AdS_5 supersymmetric black-holes. In a certain limit, these Kahler spaces take the form of cones over Sasaki spaces, which, in turn, are fibrations over toric manifolds of real dimension two. The metric on M_4 is completely determined by a single function H(x), which is the conformal factor of the two dimensional space. We study the solutions of minimal five dimensional gauged supergravity having this class of Kahler spaces as base and show that in order to generate a five dimensional solution H(x) must obey a simple sixth order differential equation. We discuss the solutions in detail, which include all known asymptotically AdS_5 black holes as well as other spacetimes with non-compact horizons. Moreover we find an infinite number of supersymmetric deformations of these spacetimes with less spatial isometries than the base space. These deformations vanish at the horizon, but become relevant asymptotically.Comment: 34 pages, 3 figures. v2: formula (8.35) and other minor typos corrected; references added; accepted for publication in JHE

Dual giant gravitons in AdSm_m ×\times Yn^n (Sasaki-Einstein)

We consider BPS motion of dual giant gravitons on Ad$S_5\times Y^5$ where $Y^5$ represents a five-dimensional Sasaki-Einstein manifold. We find that the phase space for the BPS dual giant gravitons is symplectically isomorphic to the Calabi-Yau cone over $Y^5$, with the K\"{a}hler form identified with the symplectic form. The quantization of the dual giants therefore coincides with the K\"{a}hler quantization of the cone which leads to an explicit correspondence between holomorphic wavefunctions of dual giants and gauge-invariant operators of the boundary theory. We extend the discussion to dual giants in $AdS_4 \times Y^7$ where $Y^7$ is a seven-dimensional Sasaki-Einstein manifold; for special motions the phase space of the dual giants is symplectically isomorphic to the eight-dimensional Calabi-Yau cone.Comment: 14 pages. (v2) typo's corrected; factors of AdS radius reinstated for clarity; remarks about dual giant wavefunctions in T^{1,1} expanded and put in a new subsectio

Counting 1/8-BPS Dual-Giants

We count 1/8-BPS states in type IIB string theory on AdS_5 x S^5 background which carry three independent angular momenta on S^5. These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigen states of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS_5 and one non-zero angular momentum on S^5 by considering configurations of arbitrary number of giant gravitons that share at least four supersymmetries.Comment: 19 page

1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space

We explore 1/16-BPS objects of type IIB string theory in AdS_5 * S^5. First, we consider supersymmetric AdS_5 black holes, which should be 1/16-BPS and have a characteristic that not all physical charges are independent. We point out that the Bekenstein-Hawking entropy of these black holes admits a remarkably simple expression in terms of (dependent) physical charges, which suggests its microscopic origin via certain Cardy or Hardy-Ramanujan formula. We also note that there is an upper bound for the angular momenta given by the electric charges. Second, we construct a class of 1/16-BPS giant graviton solutions in AdS_5 * S^5 and explore their properties. The solutions are given by the intersections of AdS_5 * S^5 and complex 3 dimensional holomorphic hyperspaces in C^{1+5}, the latter being the zero loci of three holomorphic functions which are homogeneous with suitable weights on coordinates. We investigate examples of giant gravitons, including their degenerations to tensionless strings.Comment: 25 pages, no figures, v2: references added, comments added in the conclusio

Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. We then use techniques from statistical mechanics to derive a scaling principle relating the specificity (binding energy) of a TF to the minimum amount of training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references adde

At the horizon of a supersymmetric AdS_5 black hole: Isometries and half-BPS giants

The near-horizon geometry of an asymptotically AdS_5 supersymmetric black hole discovered by Gutowski and Reall is analysed. After lifting the solution to 10 dimensions, we explicitly solve the Killing spinor equations in both Poincare and global coordinates. It is found that exactly four supersymmetries are preserved which is twice the number for the full black hole. The full set of isometries is constructed and the isometry supergroup is shown to be SU(1,1|1) X SU(2) X U(3). We further study half-BPS configurations of D3-branes in the near-horizon geometry in Poincare and global coordinates. Both giant graviton probes and dual giant graviton probes are found.Comment: 26 pages. v2:Typos corrected, minor change

Entropy function and attractors for AdS black holes

We apply Sen's entropy formalism to the study of the near horizon geometry and the entropy of asymptotically AdS black holes in gauged supergravities. In particular, we consider non-supersymmetric electrically charged black holes with AdS_2 xS^{d-2} horizons in U(1)^4 and U(1)^3 gauged supergravities in d=4 and d=5 dimensions, respectively. We study several cases including static/rotating, BPS and non-BPS black holes in Einstein as well as in Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole entropy are derived by extremizing the entropy function and are given entirely in terms of the gauge coupling, the electric charges and the angular momentum of the black hole.Comment: 27 pages, no figures, references adde