Abstract
We study the Standard Model with gauged $$ {\mathrm{\mathbb{Z}}}_{N=2,3,6}^{(1)} $$
ℤ
N
=
2
,
3
,
6
1
subgroups of its $$ {\mathrm{\mathbb{Z}}}_6^{(1)} $$
ℤ
6
1
1-form global symmetry, making the gauge group $$ \frac{\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)}{{\mathrm{\mathbb{Z}}}_N} $$
SU
3
×
SU
2
×
U
1
ℤ
N
. We show that, on a finite $$ {\mathbbm{T}}^3 $$
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.