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

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 $\frac{SU(3)\times SU(2)\times U(1)}{{\mathbb{Z}}_N}$. 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.

19 pages; minor typos corrected, references added, matches the published version

References in corpus (4)

• Generalized Global Symmetries
• Line Operators in the Standard Model
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• TQFT at work for IR-renormalons, resurgence and Lefschetz decomposition

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• Cobordism and Deformation Class of the Standard Model
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Proton Stability: From the Standard Model to Beyond Grand Unification
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Non-Invertible Peccei-Quinn Symmetry, Natural 2HDM Alignment, and the Visible Axion
• A Note on Proton Stability in the Standard Model