Gravity as a deformed topological gauge theory
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908749925449728 |
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| author | Thibaut, J. Lazzarini, S. |
| author_facet | Thibaut, J. Lazzarini, S. |
| contents | We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the Nieh-Yan term. Considering symmetric spaces parametrized by mutations allows to naturally obtain a bare cosmological constant which in particular cases gives rise to a positive effective cosmological constant while having an AdS spacetime.
Two examples are studied, Lorentzian geometry (including dS and AdS spacetimes) and Lorentz$\times$Weyl geometry. In the latter case we prove the equations of motion exhibit a secondary source for curvature in addition to the usual energy-momentum tensor. This additional source is expressed in terms of the spin density of matter, torsion and their variations.
Finally, we show that the gauge + matter actions constructed from invariant polynomials are asymptotically topological if one assumes a vanishing bare cosmological constant together with gauge and matter fields having compact support. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gravity as a deformed topological gauge theory Thibaut, J. Lazzarini, S. General Relativity and Quantum Cosmology Mathematical Physics 83Cxx, 70S15 We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the Nieh-Yan term. Considering symmetric spaces parametrized by mutations allows to naturally obtain a bare cosmological constant which in particular cases gives rise to a positive effective cosmological constant while having an AdS spacetime. Two examples are studied, Lorentzian geometry (including dS and AdS spacetimes) and Lorentz$\times$Weyl geometry. In the latter case we prove the equations of motion exhibit a secondary source for curvature in addition to the usual energy-momentum tensor. This additional source is expressed in terms of the spin density of matter, torsion and their variations. Finally, we show that the gauge + matter actions constructed from invariant polynomials are asymptotically topological if one assumes a vanishing bare cosmological constant together with gauge and matter fields having compact support. |
| title | Gravity as a deformed topological gauge theory |
| topic | General Relativity and Quantum Cosmology Mathematical Physics 83Cxx, 70S15 |
| url | https://arxiv.org/abs/2403.05284 |