Symmetry breaking, conformal geometry and gauge invariance

TL;DR

This paper explores the reformulation of the electroweak action using gauge-invariant variables, revealing connections between conformal geometry, gauge invariance, and the Higgs field, with implications for nonperturbative gauge fixing.

Contribution

It demonstrates that asymptotic flatness is essential for gauge invariance in this reformulation and clarifies relations to unitary gauge fixing and other gauge theories.

Findings

Asymptotic flatness avoids Gribov problems in gauge-invariant variables.

Higgs can be viewed as a conformal metric factor.

Connections between this approach and other gauge fixing methods.

Abstract

When the electroweak action is rewritten in terms of SU(2) gauge invariant variables, the Higgs can be interpreted as a conformal metric factor. We show that asymptotic flatness of the metric is required to avoid a Gribov problem: without it, the new variables fail to be nonperturbatively gauge invariant. We also clarify the relations between this approach and unitary gauge fixing, and the existence of similar transformations in other gauge theories.