Two-dimensional supersymmetric gauge theories with exceptional gauge groups

TL;DR

This paper predicts the properties of two-dimensional supersymmetric gauge theories with exceptional gauge groups using mirror symmetry, computes their Landau-Ginzburg models, and explores their IR behavior, extending known results to new gauge groups.

Contribution

It applies mirror symmetry to exceptional gauge groups, computes their mirror models, and analyzes their IR flow, providing new insights into their quantum cohomology and phase structure.

Findings

Predicted Coulomb branch relations for exceptional groups

Identified IR fixed points as free theories of twisted chiral superfields

Explored conventions and theta angle periodicities in mirror models

Abstract

We apply the recent proposal for mirrors of nonabelian (2,2) supersymmetric two-dimensional gauge theories to make predictions for two-dimensional supersymmetric gauge theories with exceptional gauge groups G2, F4, E6, E7, and E8. We compute the mirror Landau-Ginzburg models and predict excluded Coulomb loci and Coulomb branch relations (quantum cohomology). We also discuss the relationship between weight lattice normalizations and theta angle periodicities in the proposal, and explore different conventions for the mirrors. Finally, we discuss the behavior of pure gauge theories with exceptional gauge groups under RG flow, and describe evidence that any pure supersymmetric two-dimensional gauge theory with connected and simply-connected semisimple gauge group flows in the IR to a free theory of as many twisted chiral superfields as the rank of the gauge group, extending previous results for SU, SO, and Sp gauge theories.