Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups

TL;DR

This paper calculates the elliptic genera of two-dimensional N=(2,2) and N=(0,2) gauge theories with rank-one gauge groups using supersymmetric localization, providing explicit formulas and examples for various models.

Contribution

It introduces a method to compute elliptic genera for rank-one gauge theories via residue sums, extending previous techniques to new models and cases.

Findings

Derived explicit residue formulas for elliptic genera.

Applied formulas to models including the quintic Calabi-Yau and SU(2), O(2) gauge theories.

Demonstrated the method's effectiveness through concrete examples.

Abstract

We compute the elliptic genera of two-dimensional N=(2,2) and N=(0,2) gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi-Yau, N=(2,2) SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric N=(0,2) model.