Abstract
We study the Standard Model with gauged \( {\mathrm{\mathbb{Z}}}_{N=2,3,6}^{(1)} \) subgroups of its \( {\mathrm{\mathbb{Z}}}_6^{(1)} \) 1-form global symmetry, making the gauge group \( \frac{\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)}{{\mathrm{\mathbb{Z}}}_N} \). We show that, on a finite \( {\mathbbm{T}}^3 \), 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.
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Anber, M.M., Poppitz, E. Nonperturbative effects in the Standard Model with gauged 1-form symmetry. J. High Energ. Phys. 2021, 55 (2021). https://doi.org/10.1007/JHEP12(2021)055
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DOI: https://doi.org/10.1007/JHEP12(2021)055