We study the Standard Model with gauged Z(1)N=2,3,6 subgroups of its Z(1)6 1-form global symmetry, making the gauge group SU(3)×SU(2)×U(1)ZN. We show that, on a finite T3, 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.
Anber, M. M., & Poppitz, E. (2021). Nonperturbative effects in the Standard Model with gauged 1-form symmetry. Journal of High Energy Physics, 2021(12), Article 55. https://doi.org/10.1007/jhep12%282021%29055