Spontaneously Broken Subsystem Symmetries

TL;DR

This paper explores the spontaneous breaking of subsystem symmetries in continuum field theories, confirming some theories lack such breaking while introducing new models that do exhibit it under certain conditions.

Contribution

It provides a direct analysis of subsystem symmetry breaking in continuum theories and introduces novel models that can spontaneously break these symmetries.

Findings

Confirmed absence of symmetry breaking in some existing theories

Constructed new theories exhibiting spontaneous symmetry breaking

Analyzed correlation functions of charged operators

Abstract

We investigate the spontaneous breaking of subsystem symmetries directly in the context of continuum field theories by calculating the correlation function of charged operators. Our methods confirm the lack of spontaneous symmetry breaking in some of the existing continuum field theories with subsystem symmetries, as had previously been established based on a careful analysis of the spectrum. We present some novel continuum field theory constructions that do exhibit spontaneous symmetry breaking whenever allowed by general principles. These interesting patterns of symmetry breaking occur despite the fact that all the theories we study are non-interacting.