New supersymmetric index of heterotic compactifications with torsion

TL;DR

This paper calculates a new supersymmetric index for a broad class of heterotic string compactifications with torsion, using localization techniques and a geometric formula based on bundle data.

Contribution

It introduces a novel computation method for the supersymmetric index in heterotic compactifications with torsion, connecting physical and geometric data.

Findings

Explicit expression of the index as Jeffrey-Kirwan residues

A geometric formula for the index independent of specific models

Application to principal two-torus bundles over warped K3 surfaces

Abstract

We compute the new supersymmetric index of a large class of N=2 heterotic compactifications with torsion, corresponding to principal two-torus bundles over warped K3 surfaces with H-flux. Starting from a UV description as a (0,2) gauged linear sigma-model with torsion, we use supersymmetric localization techniques to provide an explicit expression of the index as a sum over the Jeffrey-Kirwan residues of the one-loop determinant. We finally propose a geometrical formula that gives the new supersymmetric index in terms of bundle data, regardless of any particular choice of underlying two-dimensional theory.