Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface

TL;DR

This paper explores the elliptic genera of K3 surfaces through mock theta functions, providing an exact Rademacher expansion for the coefficients of non-BPS representations in superconformal characters.

Contribution

It introduces a novel decomposition of K3 elliptic genera using N=4 superconformal characters and derives an exact Rademacher expansion for massive representation coefficients.

Findings

Decomposition of elliptic genus in terms of superconformal characters.

Exact Rademacher expansion for non-BPS coefficients.

Application to both compact and non-compact K3 surfaces.

Abstract

The elliptic genera of the K3 surfaces, both compact and non-compact cases, are studied by using the theory of mock theta functions. We decompose the elliptic genus in terms of the N=4 superconformal characters at level-1, and present an exact formula for the coefficients of the massive (non-BPS) representations using the Poincare-Maass series.