Lazarides-Shafi axion models as Dijkgraaf-Witten theories

TL;DR

This paper formulates a topological quantum field theory to analyze Lazarides-Shafi axion models, clarifying their symmetry structures and providing a universal formula for the domain wall number, with implications for cosmology and topological phases.

Contribution

It introduces a topological quantum field theory framework to understand Lazarides-Shafi axion models, revealing their higher-form symmetries and deriving a master formula for the domain wall number.

Findings

Derived a master formula for the domain wall number.

Identified higher-form symmetry conditions for vacuum identification.

Revealed a nontrivial four-group structure and SPT phase in the models.

Abstract

Axion models often face the domain wall problem, which threatens the standard big-bang cosmology. The Lazarides-Shafi mechanism attempts to resolve this by identifying degenerate vacua through a continuous gauge symmetry. We formulate a topological quantum field theory to isolate the essential structure of the mechanism and analyze its generalized symmetry structure, including higher-form symmetries and higher-group. This framework yields a master formula for computing the domain wall number and clarifies the higher-form symmetry conditions required for complete vacuum identification in a model independent way. Moreover, while a domain-wall-number-one scenario eliminates all higher-form global symmetries, the theory nevertheless exhibits a nontrivial four-group structure and realizes a symmetry-protected topological (SPT) phase.