Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories

TL;DR

The paper develops and applies a simple, universal framework based on $1$-instanton fermionic zero modes to detect global symmetry enhancements in $5d$ SUSY gauge theories with gauge groups $USp$, $SO$, and exceptional groups. By decomposing instantons into $SU(2)$ subgroups, counting zero modes, and enforcing gauge invariance, the author identifies conserved currents that signal symmetry enhancements and potential lifts to $6d$ via affine algebras or twisted compactifications. The results reveal systematic enhancement patterns, including $U_T(1) o SU(2)$ in many cases and various $E_n^{(1)}$ or other affine structures as well as several instances suggesting $6d$ origins. The work complements brane-web and index approaches, offering a unified route to anticipate fixed-point behaviors and guiding future exploration of higher-instanton sectors and quiver extensions.

Abstract

We study the fermionic zero modes around 1 instanton operators for 5d supersymmetric gauge theories of type USp, SO and the exceptional groups. The major motivation is to try to understand the global symmetry enhancement pattern in these theories.