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

TL;DR

This work analyzes how gauging discrete subgroups of the SM's 1-form $Z_6^{(1)}$ symmetry on a finite-volume background leads to fractional instantons with fractional topological charge that can violate baryon number. Using twisted boundary conditions on ${\mathbb T}^4$ and a self-dual, abelian ansatz, the authors derive the fractional instanton actions and topological charges, and compare their contributions to the standard BPST instantons by examining the relative suppression factors and running couplings. They find that the small hypercharge coupling strongly suppresses fractional-instanton processes unless the torus size is sub-Planckian or additional matter alters the running to raise $g_1$, and they discuss the implications for cosmology and early-universe dynamics. The results illuminate how the global structure of the SM gauge group and nonperturbative sectors in constrained volumes interplay to shape baryon- and lepton-number violation, with potential cosmological consequences if such effects were active in the early universe under suitable conditions.

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.