Instanton Number as a Symmetry

Abstract: Gauge theories in d dimensions have a (d-5)-form generalized global symmetry whose conserved charge is instanton number. In quantum gravity, we expect such symmetries to always be gauged or explicitly broken. I will discuss examples of how both can happen: gauging via Chern-Simons terms or (in 4d) massless fermions, and explicit breaking via magnetic monopoles (in both abelian and nonabelian gauge theories). In the case d=4, instanton number symmetry is a “(-1)-form U(1) symmetry,” a somewhat degenerate case. I will discuss several closely analogous properties of the cases d=4 and d>4, to argue that we should take the notion of (-1)-form symmetry seriously. I will comment on some implications of this perspective for the Strong CP problem. This talk will draw on multiple papers, including arxiv.org/abs/2012.00009 with Ben Heidenreich, Jake McNamara, Miguel Montero, Tom Rudelius, and Irene Valenzuela; arxiv.org/abs/2105.09950 with JiJi Fan, Katie Fraser, and John Stout; arxiv.org/abs/2402.00117 with Daniel Aloni, Eduardo García-Valdecasas, and Motoo Suzuki; and other work in progress.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.