Higgs Mechanism in the Presence of a Topological Term

TL;DR

This paper investigates how topological terms influence the Higgs mechanism in gauge theories, revealing that gauge fields gain mass while maintaining degrees of freedom, with a new massless scalar emerging in the spectrum.

Contribution

It demonstrates that topological terms allow gauge fields to acquire mass by absorbing multiple fields, preserving degrees of freedom, and introduces a rigorous quantization confirming the physicality of the new massless scalar.

Findings

Gauge fields become massive by 'eating' both Nambu-Goldstone and tensor fields.

A new massless scalar appears in the spectrum due to the topological term.

The number of physical degrees of freedom remains unchanged after symmetry breaking.

Abstract

In cases of both abelian and nonabelian gauge groups, we study the Higgs mechanism in the topologically massive gauge theories in an arbitrary space-time dimension. We show that when the conventional Higgs potential coexists with a topological term, gauge fields become massive by 'eating' simultaneously both the Nambu-Goldstone boson and a higher-rank tensor field, and instead a new massless scalar field is 'vomitted' in the physical spectrum. Because of the appearance of this new massless field, the number of the physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Moreover, the fact that the new field is a physical and positive norm state is rigorously proved by performing the manifestly covariant quantization of the model in three and four dimensions. In the mechanism at hand, the presence of a topological term makes it possible to shift mass of gauge fields in a nontrivial manner compared to the conventional value.