2-Group Symmetries in Class S

TL;DR

This paper reveals the presence of 2-group symmetries in 4d N=2 Class S theories, arising from the interplay of 1-form and 0-form symmetries, and provides a method to compute their structure using geometric data from compactification surfaces.

Contribution

It introduces a framework to identify and compute 2-group symmetries in Class S theories from 6d origins, linking line defects and flavor charges.

Findings

Identifies 2-group symmetries in 4d N=2 theories of Class S.

Provides a method to compute equivalence classes of line defects.

Connects 2-group structure to geometric data on Riemann surfaces.

Abstract

2-group symmetries are generalized symmetries that arise when 1-form and 0-form symmetries mix with each other. We uncover the existence of a class of 2-group symmetries in general 4d N=2 theories of Class S that can be constructed by compactifying 6d N=(2,0) SCFTs on Riemann surfaces carrying arbitrary regular punctures and outer-automorphism twist lines. The 2-group structure can be captured in terms of equivalence classes of line defects plus flavor Wilson lines, which can be thought of as accounting for screening of line defects while keeping track of flavor charges. We describe a method for computing these equivalence classes for a general Class S theory using the data on the Riemman surface used for compactifying its parent 6d N=(2,0) theory.