Spontaneously Broken Gauge Theories and the Coset Construction

TL;DR

This paper explores how coset construction methods can be applied to spontaneously broken gauge theories, particularly Yang-Mills theories, revealing natural derivations of massive gauge bosons and connections to St"uckelberg fields.

Contribution

It demonstrates that coset techniques can effectively describe low energy physics in broken gauge theories and naturally incorporate St"uckelberg fields, with potential applications to massive gravity.

Findings

Coset methods reproduce massive gauge boson descriptions.

St"uckelberg replacement arises naturally in the framework.

Potential extensions to p-form fields and massive gravity.

Abstract

The methods of non-linear realizations have proven to be powerful in studying the low energy physics resulting from spontaneously broken internal and spacetime symmetries. In this paper, we reconsider how these techniques may be applied to the case of spontaneously broken gauge theories, concentrating on Yang-Mills theories. We find that coset methods faithfully reproduce the description of low energy physics in terms of massive gauge bosons and discover that the St\"uckelberg replacement commonly employed when treating massive gauge theories arises in a natural manner. Uses of the methods are considered in various contexts, including generalizations to $p$-form gauge fields. We briefly discuss potential applications of the techniques to theories of massive gravity and their possible interpretation as a Higgs phase of general relativity.