Gauging the Standard Model 1-form symmetry via gravitational instantons
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917282471477248 |
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| author | Anber, Mohamed M. |
| author_facet | Anber, Mohamed M. |
| contents | We investigate the fate of the Standard Model (SM) $\mathbb Z_6^{(1)}$ electric $1$-form global symmetry in the background of gravitational instantons, focusing on Eguchi-Hanson (EH) geometries. We show that EH instantons support quantized $\mathbb Z_6^{(1)}$ fluxes localized on their $S^2$ bolt, inducing fractional topological charge without backreacting on the geometry. The requirement that quark and lepton wavefunctions be globally well-defined under parallel transport imposes boundary conditions, removing ill-defined fermion zero modes; the surviving spectrum is confirmed by an explicit solution of the Dirac equation and by the Atiyah-Patodi-Singer index theorem. The Euclidean path integral in the EH background can be interpreted as a transition amplitude from an entangled state between two identical halves of space to the vacuum. Summing over all $\mathbb{Z}_6^{(1)}$ flux sectors in the path integral gauges the SM $1$-form symmetry; thus, it cannot persist as an exact global symmetry in the semiclassical limit of gravity. We further show that these fluxes induce baryon- and lepton-number violating processes, which are exponentially suppressed due to the smallness of the hypercharge coupling constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauging the Standard Model 1-form symmetry via gravitational instantons Anber, Mohamed M. High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We investigate the fate of the Standard Model (SM) $\mathbb Z_6^{(1)}$ electric $1$-form global symmetry in the background of gravitational instantons, focusing on Eguchi-Hanson (EH) geometries. We show that EH instantons support quantized $\mathbb Z_6^{(1)}$ fluxes localized on their $S^2$ bolt, inducing fractional topological charge without backreacting on the geometry. The requirement that quark and lepton wavefunctions be globally well-defined under parallel transport imposes boundary conditions, removing ill-defined fermion zero modes; the surviving spectrum is confirmed by an explicit solution of the Dirac equation and by the Atiyah-Patodi-Singer index theorem. The Euclidean path integral in the EH background can be interpreted as a transition amplitude from an entangled state between two identical halves of space to the vacuum. Summing over all $\mathbb{Z}_6^{(1)}$ flux sectors in the path integral gauges the SM $1$-form symmetry; thus, it cannot persist as an exact global symmetry in the semiclassical limit of gravity. We further show that these fluxes induce baryon- and lepton-number violating processes, which are exponentially suppressed due to the smallness of the hypercharge coupling constant. |
| title | Gauging the Standard Model 1-form symmetry via gravitational instantons |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.22788 |