Gravity with torsion as deformed $BF$ theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911937061715968 |
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| author | Cattaneo, Alberto S. Menger, Leon Schiavina, Michele |
| author_facet | Cattaneo, Alberto S. Menger, Leon Schiavina, Michele |
| contents | We study a family of (possibly non topological) deformations of $BF$ theory for the Lie algebra obtained by quadratic extension of $\mathfrak{so}(3,1)$ by an orthogonal module. The resulting theory, called quadratically extended General Relativity (qeGR), is shown to be classically equivalent to certain models of gravity with dynamical torsion. The classical equivalence is shown to promote to a stronger notion of equivalence within the Batalin--Vilkovisky formalism. In particular, both Palatini--Cartan gravity and a deformation thereof by a dynamical torsion term, called (quadratic) generalised Holst theory, are recovered from the standard Batalin--Vilkovisky formulation of qeGR by elimination of generalised auxiliary fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01877 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gravity with torsion as deformed $BF$ theory Cattaneo, Alberto S. Menger, Leon Schiavina, Michele Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 83C47, 57R56, 81T70 We study a family of (possibly non topological) deformations of $BF$ theory for the Lie algebra obtained by quadratic extension of $\mathfrak{so}(3,1)$ by an orthogonal module. The resulting theory, called quadratically extended General Relativity (qeGR), is shown to be classically equivalent to certain models of gravity with dynamical torsion. The classical equivalence is shown to promote to a stronger notion of equivalence within the Batalin--Vilkovisky formalism. In particular, both Palatini--Cartan gravity and a deformation thereof by a dynamical torsion term, called (quadratic) generalised Holst theory, are recovered from the standard Batalin--Vilkovisky formulation of qeGR by elimination of generalised auxiliary fields. |
| title | Gravity with torsion as deformed $BF$ theory |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 83C47, 57R56, 81T70 |
| url | https://arxiv.org/abs/2310.01877 |