Emergent 1-form symmetries

TL;DR

This paper investigates the conditions under which 1-form symmetries can emerge at long distances despite being broken at short scales, with implications for QCD and confinement phenomena.

Contribution

It identifies key criteria for emergent 1-form symmetries, including the role of topological operators and their correlation functions, and discusses their relation to anomalies and confinement.

Findings

Emergent 1-form symmetries require operators becoming topological at long distances.

Spontaneous breaking or 't Hooft anomalies facilitate emergence of 1-form symmetries.

Confinement phase is nearly incompatible with the emergence of 1-form symmetries.

Abstract

We explore the necessary conditions for 1-form symmetries to emerge in the long-distance limit when they are explicitly broken at short distances. A minimal requirement is that there exist operators which become topological at long distances and that these operators have non-trivial correlation functions. These criteria are obeyed when the would-be emergent symmetry is spontaneously broken, or is involved in 't Hooft anomalies. On the other hand, confinement, i.e. a phase with unbroken 1-form symmetry, is nearly incompatible with the emergence of 1-form symmetries. We comment on some implications of our results for QCD as well as the idea of Higgs-confinement continuity.