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

TL;DR

This paper studies 5d supersymmetric quiver gauge theories with ADE Dynkin diagram structures, identifying conditions for symmetry enhancement via instanton operators and exploring connections to 6d superconformal theories.

Contribution

It provides general rules for symmetry enhancement in 5d $SU(N)$ quiver theories based on instanton operators and flavor content, including cases with symmetric matter.

Findings

Symmetry enhancement to $G imes G$ or subgroups under specific flavor conditions.

Identification of theories as compactifications of 6d superconformal theories.

Analysis of theories with symmetric and antisymmetric hypermultiplets.

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 $\kappa_i$ and additional $w_i$ fundamentals. When the total flavor number at each node is less than or equal to $2N_i-2|\kappa_i|$, 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.