Gauge symmetry breaking in gauge theories---In search of clarification

TL;DR

This paper critically examines the concept of spontaneous gauge symmetry breaking in gauge theories, highlighting discrepancies between common textbook explanations and rigorous theoretical frameworks, and discusses philosophical implications.

Contribution

It clarifies the distinction between physical symmetry breaking and gauge fixing artifacts, emphasizing the role of remnant symmetries and phase transitions in gauge theories.

Findings

Elitzur's theorem rigorously prohibits local gauge symmetry breaking.

Gauge symmetry breaking occurs in remnant subgroups after gauge fixing.

The paper offers philosophical insights into the interpretation of gauge symmetries.

Abstract

The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by our leading theoretical frameworks of gauge quantum theories. In the context of lattice gauge theory, the statement that local gauge symmetry cannot be spontaneously broken can even be made rigorous in the form of Elitzur's theorem. Nevertheless, gauge symmetry breaking does occur in gauge quantum field theories in the form of the breaking of remnant subgroups of the original local gauge group under which the theories typically remain invariant after gauge fixing. The paper discusses the relation between these instances of symmetry breaking and phase transitions and draws some more general conclusions for the philosophical interpretation of gauge symmetries and their breaking.