Central extensions of higher groups: Green-Schwarz mechanism and 2-connections

TL;DR

This paper explores the structure of smooth 2-groups in quantum field theory, linking them to Chern--Simons levels and the Green-Schwarz mechanism, and proposes the potential for smooth infinity-group symmetries.

Contribution

It introduces a framework for understanding 2-group structures via central extensions and fixes issues using the bibundle model, also discussing principal 2-connection theory and higher symmetries.

Findings

2-group structures are guaranteed by Chern--Simons levels

The bibundle model can fix current 2-group problems

Proposes the existence of smooth infinity-group symmetries

Abstract

We study the smooth $2$-group structure arising in the presence of quantum field theory with one-form symmetry. We acquire $2$-group structures obtained by a central extension of the zero-form symmetry by the one-form symmetry. We determine that the existence of a $2$-group structure is guaranteed by Chern--Simons levels. We further verify how we will be able to provide a fix to the current $2$-group problems by using the bibundle model. We outline the principal $2$-connection theory with respect to such $2$-group and compare it with the ansatz obtained from the Green--Schwarz mechanism. We further propose the existence of smooth $\infty$-group symmetries in quantum field theory.