Spontaneously Broken $(-1)$-Form U(1) Symmetries

TL;DR

This paper introduces the concept of spontaneously broken $(-1)$-form U(1) symmetries, linking them to the Strong CP problem in QCD and providing a new perspective on symmetry breaking phenomena.

Contribution

It extends the notion of symmetry breaking to $(-1)$-form symmetries and reinterprets the Strong CP problem as a consequence of spontaneously broken instantonic symmetry.

Findings

Vacuum energy depends on background field $ heta$

Reinterpretation of the Strong CP problem

Unification of known solutions within this framework

Abstract

Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to $(-1)$-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field $\theta$, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. We discuss how known solutions to the problem are unified in this framework and explore some, so far unsuccessful, attempts to find new solutions.