Axions, Higher-Groups, and Emergent Symmetry

TL;DR

This paper explores the complex higher-form symmetries of axions, revealing a higher-group structure that constrains the energy scales of symmetry emergence and decay processes in axion-related theories.

Contribution

It uncovers the higher-group symmetry structure of axions and derives universal constraints on renormalization group flows and infrared symmetry emergence.

Findings

Higher-form symmetries of axions form a higher-group structure.

Universal inequalities relate energy scales of axion string decay and charged particle masses.

Constraints apply to UV completions of axion-Yang-Mills theories.

Abstract

Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give universal inequalities on the energy scales where various infrared symmetries emerge. For example, we show that in any UV completion of axion-Yang-Mills, the energy scale at which axion strings can decay is always larger than the mass scale of charged particles.