Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories

TL;DR

This work provides a practical criterion for ultraviolet symmetry enhancement in 5d supersymmetric gauge theories by analyzing the fermionic zero modes of one-instanton operators. By mapping the zero-mode structure to broken current supermultiplets, the author derives when instanton-induced currents enhance flavor symmetries and how these patterns signal UV completions to either 5d or 6d (on S^1) theories. The method is applied to SU(2) and SU(N) theories with various matter contents and extended to quiver gauge theories, revealing enhancements corresponding to SO(2N_f), E_{N_f+1}, affine E8, and other Dynkin-type symmetries; in quivers, instanton currents organize into gauge- and flavor-symmetry structures tied to Dynkin diagrams and their affine extensions. The results align with known results from string theory and 6d-compactification perspectives, offering a streamlined framework to diagnose UV completions and symmetry enhancements in a broad class of 5d SCFTs and their infrared gauge theory descriptions.

Abstract

Supersymmetric gauge theories in five dimensions often exhibit less symmetry than the ultraviolet fixed points from which they flow. The fixed points might have larger flavor symmetry or they might even be secretly six-dimensional theories on S^1. Here we provide a simple criterion when such symmetry enhancement in the ultraviolet should occur, by a direct study of the fermionic zero modes around one-instanton operators.