Field theories with higher-group symmetry from composite currents

TL;DR

This paper demonstrates how higher-group symmetries naturally arise in physical systems with multiple spontaneously broken symmetries, expanding understanding beyond traditional direct product symmetry descriptions.

Contribution

It introduces a bottom-up approach to derive higher-group symmetries from low-energy theories with multiple broken symmetries, linking to physical examples like superfluid mixtures.

Findings

Higher-group symmetry emerges from multiple broken symmetries.

Hierarchy of topological currents forms a higher-group structure.

Physical systems like superfluid mixtures exhibit these symmetries.

Abstract

Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed 't Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.