N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

TL;DR

This paper explores the elliptic genera of hyperKahler manifolds through N=4 superconformal algebra representation theory, revealing an entropy concept linked to their geometry, matching black hole entropy in specific cases.

Contribution

It introduces a novel approach to relate hyperKahler manifold geometry with entropy via N=4 superconformal algebra and elliptic genus decomposition.

Findings

Exponential growth of BPS state multiplicities suggests an entropy measure.

Entropy of symmetric product of K3 surfaces matches D5-D1 black hole entropy.

Rademacher expansion used to analyze multiplicity increase rate.

Abstract

We study the elliptic genera of hyperKahler manifolds using the representation theory of N=4 superconformal algebra. We consider the decomposition of the elliptic genera in terms of N=4 irreducible characters, and derive the rate of increase of the multiplicities of half-BPS representations making use of Rademacher expansion. Exponential increase of the multiplicity suggests that we can associate the notion of an entropy to the geometry of hyperKahler manifolds. In the case of symmetric products of K3 surfaces our entropy agrees with the black hole entropy of D5-D1 system.