2-Group Symmetries and their Classification in 6d

TL;DR

This paper identifies and classifies 2-group symmetries in 6d superconformal field theories, revealing how discrete and continuous symmetries can intertwine, and provides a computational tool for analyzing such symmetries across dimensions.

Contribution

It introduces a classification of 6d superconformal theories with 2-group symmetries and extends the methodology to other dimensions with a computational tool.

Findings

Classification of 6d SCFTs with 2-group symmetries

Development of a Mathematica code for symmetry computation

Discussion of mixed 't Hooft anomalies in 6d

Abstract

We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field theories with such 2-group symmetries. The approach taken in 6d is applicable more generally, with minor modifications to include dimension specific operators (such as instantons in 5d and monopoles in 3d), and we provide a discussion of the dimension-independent aspects of the analysis. We include an ancillary mathematica code for computing 2-group symmetries, once the dimension specific input is provided. We also discuss a mixed 't Hooft anomaly between discrete 0-form and 1-form symmetries in 6d.