The Abelian Topological Mass Mechanism From Dimensional Reduction

TL;DR

This paper demonstrates how the abelian topological mass mechanism in four dimensions can be derived from a five-dimensional gauge-invariant action through dimensional reduction, connecting various formulations of massive spin-1 fields.

Contribution

It introduces a novel derivation of the Cremmer-Sherk topological mass mechanism from five-dimensional theories, unifying different descriptions of massive gauge fields.

Findings

Derived the 4D topological mass mechanism from 5D gauge theories.

Revealed the dual equivalence between vector and antisymmetric fields in 5D.

Recovered the Kalb-Ramond and Stuckelberger formulations for massive spin-1.

Abstract

We show that the abelian topological mass mechanism in four dimensions, described by the Cremmer-Sherk action, can be obtained from dimensional reduction in five dimensions. Starting from a gauge invariant action in five dimensions, where the dual equivalence between a massless vector field and a massless second-rank antisymmetric field in five dimensions is established, the dimensional reduction is performed keeping only one massive mode. Furthermore, the Kalb-Ramond action and the Stuckelberger formulation for massive spin-1 are recovered.