Dressed elliptic genus of heterotic compactifications with torsion and general bundles

TL;DR

This paper defines and computes the dressed elliptic genus for heterotic compactifications with torsion, incorporating general bundles, using supersymmetric localization and mathematical techniques, with implications for moonshine phenomena in string theory.

Contribution

It introduces a comprehensive definition of the dressed elliptic genus for heterotic torsional compactifications with general bundles, extending previous work and linking to N=4 superconformal characters.

Findings

Derived a formula for the dressed elliptic genus using localization.

Proved the equivalence of physical and mathematical definitions.

Decomposed the genus into N=4 superconformal characters, suggesting moonshine connections.

Abstract

We define and compute the dressed elliptic genus of N = 2 heterotic compactifications with torsion that are principal two-torus bundles over a K3 surface. We consider the most general gauge bundle compatible with supersymmetry, a stable holomorphic vector bundle over the base together with an Abelian bundle over the total space, generalizing the computation previously done by the authors in the absence of the latter. Starting from a (0,2) gauged linear sigma-model with torsion we use supersymmetric localization to obtain the result. We provide also a mathematical definition of the dressed elliptic genus as a modified Euler characteristic and prove that both expressions agree for hypersurfaces in weighted projective spaces. Finally we show that it admits a natural decomposition in terms of N = 4 superconformal characters, that may be useful to investigate moonshine phenomena for this wide class of N = 2 vacua, that includes K3*T2 compactifications as special cases.