CMSA Quantum Matter in Mathematics and Physics: Spontaneously Broken (-1)-form symmetries

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 constant background field θ, 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. I will also talk about our ongoing work on the explicit breaking by monopoles.