Superconformal Quantum Mechanics of Small Black Holes

TL;DR

This paper supports the holographic duality between superconformal quantum mechanics and small black holes by matching state counts with black hole entropy in specific string theory setups.

Contribution

It extends the superconformal quantum mechanics framework to small black holes with vanishing horizons, providing evidence for the duality in new cases.

Findings

Asymptotic growth of chiral primaries matches black hole entropy.

State counting reduces to Landau levels and cohomology classes.

Supports holographic duality for small black holes.

Abstract

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 $M$.