Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups

TL;DR

This paper develops a systematic method to compute elliptic genera for 2D supersymmetric pure gauge theories with semisimple, non-simply-connected gauge groups, and applies it to low-rank examples, confirming theoretical expectations.

Contribution

It introduces a new systematic approach for calculating elliptic genera in 2D gauge theories with non-simply-connected gauge groups and discrete theta angles, extending previous methods.

Findings

Results align with decomposition of theories with finite global one-form symmetries.

Consistent with supersymmetry breaking patterns for certain discrete theta angles.

Predictions for elliptic genera of remaining pure gauge theories based on decomposition.

Abstract

In this paper we describe a systematic method to compute elliptic genera of (2,2) supersymmetric gauge theories in two dimensions with gauge group G/Gamma (for G semisimple and simply-connected, Gamma a subgroup of the center of G) with various discrete theta angles. We apply the technique to examples of pure gauge theories with low-rank gauge groups. Our results are consistent with expectations from decomposition of two-dimensional theories with finite global one-form symmetries and with computations of supersymmetry breaking for some discrete theta angles in pure gauge theories. Finally, we make predictions for the elliptic genera of all the other remaining pure gauge theories by applying decomposition and matching to known supersymmetry breaking patterns.