Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

TL;DR

The paper develops a systematic framework to diagnose symmetry enhancement in 5d $\mathrm{SU}(N)$ quiver gauge theories whose nodes form ADE Dynkin diagrams, mediated by instanton currents. It introduces a practical rule set using two copies of the Dynkin diagram, Dyn_+ and Dyn_-, to determine the non-abelian part of the UV symmetry and identifies when affine structures arise, signaling 6d $SCFT$ uplifts via $S^1$ reductions. The analysis covers generic bifundamental matter as well as hypermultiplets in anti-symmetric and symmetric representations, and extends to $SU(2)$ endpoints with subtle theta-angle effects, mass deformations, and RG flows. The results connect a broad class of 5d quivers to known or conjectured 6d SCFTs realized in string/F-theory, providing a diagnostic for UV completeness and a blueprint for classifying these theories according to their symmetry enhancements and potential higher-dimensional origins.

Abstract

We consider general 5d $SU(N)$ quiver gauge theories whose nodes form an ADE Dynkin diagram of type $G$. Each node has $SU(N_i)$ gauge group of general rank, Chern-Simons level $κ_i$ and additional $w_i$ fundamentals. When the total flavor number at each node is less than or equal to $2N_i-2|κ_i|$, we give general rules under which the symmetries associated to instanton currents are enhanced to $G \times G$ or a subgroup of it in the UV 5d superconformal theory. When the total flavor number violates that condition at some of the nodes, further enhancement of flavor symmetries occurs. In particular we find a large class of gauge theories interpreted as $S^1$ compactification of 6d superconformal theories which are waiting for string/F-theory realization. We also consider hypermultiplets in (anti-)symmetric representation.