Generating Jackiw-Teitelboim Euclidean gravity from static three-dimensional Maxwell-Chern-Simons electromagnetism
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908553418113024 |
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| author | Bittencourt, Thales F. Sobreiro, Rodrigo F. |
| author_facet | Bittencourt, Thales F. Sobreiro, Rodrigo F. |
| contents | We consider pure three-dimensional Maxwell-Chern-Simons electrodynamics in the static limit. We show that this theory can be mapped onto a two-dimensional gravitational model in the first-order formalism of Riemannian manifolds with Euclidean signature, coupled to a real scalar field naturally interpreted as a dilaton. In this framework, the Newtonian and cosmological constants in two dimensions are fully determined by the electric charge. The solution to this gravitational model is found to be trivial: a constant dilaton field on a flat manifold. However, we introduce two distinct shifts of the spin-connection that transform the model into Jackiw-Teitelboim gravity. Specifically, we identify two additional solutions: a hyperbolic manifold with also a constant dilaton configuration; and a spherical manifold where, again, the dilaton assumes a constant, nonzero field configuration. In both non-flat cases, by employing the Gauss-Bonnet theorem in the specific cases of compact manifolds, we establish that the manifold's radius is fixed by the cosmological constant (and, therefore, by the electric charge). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generating Jackiw-Teitelboim Euclidean gravity from static three-dimensional Maxwell-Chern-Simons electromagnetism Bittencourt, Thales F. Sobreiro, Rodrigo F. High Energy Physics - Theory General Relativity and Quantum Cosmology We consider pure three-dimensional Maxwell-Chern-Simons electrodynamics in the static limit. We show that this theory can be mapped onto a two-dimensional gravitational model in the first-order formalism of Riemannian manifolds with Euclidean signature, coupled to a real scalar field naturally interpreted as a dilaton. In this framework, the Newtonian and cosmological constants in two dimensions are fully determined by the electric charge. The solution to this gravitational model is found to be trivial: a constant dilaton field on a flat manifold. However, we introduce two distinct shifts of the spin-connection that transform the model into Jackiw-Teitelboim gravity. Specifically, we identify two additional solutions: a hyperbolic manifold with also a constant dilaton configuration; and a spherical manifold where, again, the dilaton assumes a constant, nonzero field configuration. In both non-flat cases, by employing the Gauss-Bonnet theorem in the specific cases of compact manifolds, we establish that the manifold's radius is fixed by the cosmological constant (and, therefore, by the electric charge). |
| title | Generating Jackiw-Teitelboim Euclidean gravity from static three-dimensional Maxwell-Chern-Simons electromagnetism |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2503.19803 |