Gauge invariance for the massive axion

TL;DR

This paper develops a gauge-invariant framework for massive axions involving scalar and antisymmetric fields, exploring their duality and topological properties, and highlighting differences on complex manifolds.

Contribution

It introduces a gauge-invariant formulation for massive axions and analyzes their duality and topological distinctions from non-gauge invariant models.

Findings

Gauge-invariant formulation for massive axions established.

Duality with non-gauge invariant models confirmed locally.

Differences identified on manifolds with non-trivial topology.

Abstract

A massive gauge invariant formulation for scalar ($\phi$) and antisymmetric ($C_{mnp}$) fields with a topological coupling, which provides a mass for the axion field, is considered. The dual and local equivalence with the non-gauge invariant proposal is established, but on manifolds with non-trivial topological structure both formulations are not globally equivalent.