Nonperturbative effects in the Standard Model with gauged 1-form symmetry

TL;DR

This paper investigates the effects of gauging certain 1-form symmetries in the Standard Model, revealing the existence of fractional instantons on finite tori that can violate baryon and lepton numbers, with implications for cosmology.

Contribution

It demonstrates the presence of fractional instantons in the gauged Standard Model and analyzes their impact on baryon and lepton number violation, comparing them to traditional instantons.

Findings

Fractional instantons exist on finite tori in the gauged Standard Model.

Their contributions are suppressed by small hypercharge coupling unless certain conditions are met.

Implications for cosmological bounds on the size of the universe.

Abstract

We study the Standard Model with gauged $\mathbb Z_{N=2,3,6}^{(1)}$ subgroups of its $\mathbb Z_6^{(1)}$ 1-form global symmetry, making the gauge group $SU(3) \times SU(2)\times U(1) \over \mathbb Z_N$. We show that, on a finite $\mathbb T^3$, there are self-dual instantons of fractional topological charge. They mediate baryon- and lepton-number violating processes. We compare their amplitudes to the ones due to the usual BPST-instantons. We find that the small hypercharge coupling suppresses the fractional-instanton contribution, unless the torus size is taken sub-Planckian, or extra matter is added above the weak scale. We also discuss these results in light of the cosmological bounds on the torus size.