Black Holes and Abelian Instantons
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909964637831168 |
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| author | Garcia, Isabel Garcia Maderazo, Elliot |
| author_facet | Garcia, Isabel Garcia Maderazo, Elliot |
| contents | We argue that the electromagnetic $θ$-term is a physical parameter of the Standard Model coupled to gravity. Specifically, in the context of 4-dimensional Einstein-Maxwell theory we show that there exist Euclidean field configurations that have finite action, are asymptotically flat, and feature non-zero electromagnetic second Chern number. These ``gravitational Abelian instantons" correspond to a dyonic extension of a Euclidean wormhole. We argue that these configurations should be included in the gravitational path integral, and that doing so generates a non-perturbative contribution to the vacuum energy density that is $θ$-dependent. We provide a Lorentzian interpretation of these instantons as capturing the effect of quantum fluctuations corresponding to pair production and annihilation of charged black holes. When $θ$ is the expectation value of a dynamical axion field, the instantons presented here generate a potential for the axion, thereby breaking the axion shift symmetry. This provides yet another example of how quantum gravity violates global symmetries through the existence of black holes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Black Holes and Abelian Instantons Garcia, Isabel Garcia Maderazo, Elliot High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology We argue that the electromagnetic $θ$-term is a physical parameter of the Standard Model coupled to gravity. Specifically, in the context of 4-dimensional Einstein-Maxwell theory we show that there exist Euclidean field configurations that have finite action, are asymptotically flat, and feature non-zero electromagnetic second Chern number. These ``gravitational Abelian instantons" correspond to a dyonic extension of a Euclidean wormhole. We argue that these configurations should be included in the gravitational path integral, and that doing so generates a non-perturbative contribution to the vacuum energy density that is $θ$-dependent. We provide a Lorentzian interpretation of these instantons as capturing the effect of quantum fluctuations corresponding to pair production and annihilation of charged black holes. When $θ$ is the expectation value of a dynamical axion field, the instantons presented here generate a potential for the axion, thereby breaking the axion shift symmetry. This provides yet another example of how quantum gravity violates global symmetries through the existence of black holes. |
| title | Black Holes and Abelian Instantons |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.13833 |