Elliptic genera of 2d N=2 gauge theories

TL;DR

This paper provides a formula for computing elliptic genera of 2D N=(2,2) and N=(0,2) gauge theories using Jeffrey-Kirwan residues, with examples and duality discussions.

Contribution

It introduces a residue-based formula for elliptic genera of 2D gauge theories, extending previous work and including non-Abelian cases and dualities.

Findings

Derived a residue formula for elliptic genera.

Applied the formula to Abelian and non-Abelian theories.

Discussed dualities in U(k) and SU(k) gauge theories.

Abstract

We compute the elliptic genera of general two-dimensional N=(2,2) and N=(0,2) gauge theories. We find that the elliptic genus is given by the sum of Jeffrey-Kirwan residues of a meromorphic form, representing the one-loop determinant of fields, on the moduli space of flat connections on T^2. We give several examples illustrating our formula, with both Abelian and non-Abelian gauge groups, and discuss some dualities for U(k) and SU(k) theories. This paper is a sequel to the authors' previous paper arXiv:1305.0533.