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

We study the Standard Model with gauged Z(N=2,3,6)((1)) subgroups of its Z(6)((1)) 1-form global symmetry, making the gauge group SU(3)xSU(2)xU(1)/Z(N). We show that, on a finite 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.