2-Group Symmetries and M-Theory

TL;DR

This paper develops methods to determine 2-group symmetries in M-theory engineered quantum field theories, especially in complex geometric backgrounds, confirming and extending previous geometric engineering results.

Contribution

It introduces techniques to extract 2-group symmetry structures from boundary geometries in M-theory, applicable even to non-Lagrangian 5d theories.

Findings

Methods successfully determine 2-group structures from boundary geometries.

Application to toric Calabi-Yau cones confirms previous geometric engineering results.

Extends understanding of 2-groups in non-Lagrangian theories.

Abstract

Quantum Field Theories engineered in M-theory can have 2-group symmetries, mixing 0-form and 1-form symmetry backgrounds in non-trivial ways. In this paper we develop methods for determining the 2-group structure from the boundary geometry of the M-theory background. We illustrate these methods in the case of 5d theories arising from M-theory on ordinary and generalised toric Calabi-Yau cones, including cases in which the resulting theory is non-Lagrangian. Our results confirm and elucidate previous results on 2-groups from geometric engineering.