Superconformal Black Hole Quantum Mechanics

In recent work, the superconformal quantum mechanics describing D0 branes in the AdS_2xS^2xCY_3 attractor geometry of a Calabi-Yau black hole with D4 brane charges p^A has been constructed and found to contain a large degeneracy of chiral primary bound states. In this paper it is shown that the asymptotic growth of chiral primaries for N D0 branes exactly matches the Bekenstein-Hawking area law for a black hole with D4 brane charge p^A and D0 brane charge N. This large degeneracy arises from D0 branes in lowest Landau levels which tile the CY_3xS^2 horizon. It is conjectured that such a multi-D0 brane CFT1 is holographically dual to IIA string theory on AdS_2xS^2xCY_3.Comment: 8 page

Superconformal Quantum Mechanics of Small Black Holes

Recently, Gaiotto, Strominger and Yin have proposed a holographic dual description for the near-horizon physics of certain N=2 black holes in terms of the superconformal quantum mechanics on D0-branes in the attractor geometry. We provide further evidence for their proposal by applying it to the case of `small' black holes which have vanishing horizon area in the leading supergravity approximation. We consider 2-charge black holes in type IIA on $T^2 \times M$, where $M$ can be either $K_3$ or $T^4$, made up out of D0-branes and D4-branes wrapping $M$. We construct the corresponding superconformal quantum mechanics and show that the asymptotic growth of chiral primaries exactly matches with the known entropy of these black holes. The state-counting problem reduces to counting lowest Landau levels on $T^2$ and Dolbeault cohomology classes on $M$.Comment: Latex, 16 pages; v2: minor corrections, references added, published versio

AdS Taub-Nut Space and the O(N) Vector Model on a Squashed 3-Sphere

In this note, motivated by the Klebanov-Polyakov conjecture we investigate the strongly coupled O(N) vector model at large $N$ on a squashed three-sphere and its holographic relation to bulk gravity on asymptotically locally $AdS_4$ spaces. We present analytical results for the action of the field theory as the squashing parameter $\alpha\to-1$, when the boundary becomes effectively one dimensional. The dual bulk geometry is AdS-Taub-NUT space in the corresponding limit. In this limit we solve the theory exactly and show that the action of the strongly coupled boundary theory scales as $\ln(1+\alpha)/ (1+\alpha)^2$. This result is remarkably close to the $-1/(1+\alpha)^2$ scaling of the Einstein gravity action for AdS-Taub-NUT space. These results explain the numerical agreement presented in hep-th/0503238, and the soft logarithmic departure is interpreted as a prediction for the contribution due to higher spin fields in the bulk $AdS_4$ geometry.Comment: 11 pages, 3 figures. References adde

Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics

The twisting function describing a nonstandard (super-Jordanian) quantum deformation of $osp(1|2)$ is given in explicite closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed $osp(1|2)$ superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal algebra, which can be applied as a symmetry algebra of N=1 superconformal mechanics.Comment: 13 pages,LaTeX, v2. References added, typos correcte

N=4 superconformal mechanics as a Non linear Realization

An action for a superconformal particle is constructed using the non linear realization method for the group PSU(1,1|2), without introducing superfields. The connection between PSU(1,1|2) and black hole physics is discussed. The lagrangian contains six arbitrary constants and describes a non-BPS superconformal particle. The BPS case is obtained if a precise relation between the constants in the lagrangian is verified, which implies that the action becomes kappa-symmetric.Comment: new subection, references added and new acknowledgment

Black Holes in Supergravity and String Theory

We give an elementary introduction to black holes in supergravity and string theory. The focus is on BPS solutions in four- and higher-dimensional supergravity and string theory. Basic ideas and techniques are explained in detail, including exercises with solutions.Comment: 64 pages, based on lectures given at the school of the TMR network 'Quantum aspects of gauge theories, supersymmetry and unification' in Torino, January 26 - February 2, 2000. To be published in Class. Quant. Grav. (Some typos corrected, two references added.