Vacuum Geometry

TL;DR

This paper explores the geometric structure of vacuum manifolds in gauge theories, revealing how two natural metrics influence symmetry breaking and its non-perturbative phenomena.

Contribution

It introduces and analyzes two natural metrics on the vacuum manifold, highlighting their role in the non-perturbative aspects of symmetry breaking.

Findings

Identification of two distinct metrics on the vacuum manifold

The interplay between metrics affects symmetry breaking features

Insights into non-perturbative phenomena in gauge theories

Abstract

We analyse symmetry breaking in general gauge theories paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: a Euclidean metric associated with the scalar sector, and another generally inequivalent metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of symmetry breaking.