Comments on the twisted punctures of $A_\text{even}$ class S theory

TL;DR

This paper reveals a global anomaly in the USp symmetry of a specific class S theory with twisted punctures, impacting the understanding of its UV completion and symmetry properties.

Contribution

It identifies a global anomaly in the USp symmetry of twisted punctures in class S theories of type A_even and explores its implications for related superconformal theories.

Findings

USp symmetry has a $bZ_2$ global anomaly.

The $R_{2,2N}$ theory can be seen as a UV completion of an SO(2N+1) gauge theory.

The anomaly affects the symmetry structure of the superconformal field theory.

Abstract

We point out that the $\text{USp}$ symmetry associated to a full twisted puncture of a class S theory of type $A_\text{even}$ has the global anomaly associated to $\pi_4(\text{USp})=\mathbb{Z}_2$. We discuss manifestations of this fact in the context of the superconformal field theory $R_{2,2N}$ introduced by Chacaltana, Distler and Trimm. For example, we find that this theory can be thought of as a natural ultraviolet completion of an infrared-free $\text{SO}(2N+1)$ gauge theory with $2N$ flavors, whose $\text{USp}(4N)$ symmetry clearly has the global anomaly.