Massive bigravity as a presymplectic BV-AKSZ sigma-model
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| Format: | Preprint |
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2024
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| _version_ | 1866916544507805696 |
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| author | Grigoriev, Maxim Gritzaenko, Vyacheslav |
| author_facet | Grigoriev, Maxim Gritzaenko, Vyacheslav |
| contents | We propose a presymplectic BV-AKSZ sigma model encoding the ghost-free massive bigravity theory action as well as its Batalin-Vilkovisky extension in terms of the finite-dimensional graded geometry of the target space. A characteristic feature of the construction is that the target space is realised as a quasi-regular submanifold of a linear graded manifold which, in turn, is a direct product of two copies of the shifted Poincaré or (anti-)de Sitter Lie algebra. This graded manifold comes equipped with a natural presymplectcic structure and the compatible pre-$Q$ structure which is a sum of the Chevalley-Eilenberg differentials of each copy of the Lie algebra and the interaction term. The constraints determining the submanifold are the supergeometrical realisation of the known Deser-van Nieuwenhuizen condition and its descendant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_13075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Massive bigravity as a presymplectic BV-AKSZ sigma-model Grigoriev, Maxim Gritzaenko, Vyacheslav High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We propose a presymplectic BV-AKSZ sigma model encoding the ghost-free massive bigravity theory action as well as its Batalin-Vilkovisky extension in terms of the finite-dimensional graded geometry of the target space. A characteristic feature of the construction is that the target space is realised as a quasi-regular submanifold of a linear graded manifold which, in turn, is a direct product of two copies of the shifted Poincaré or (anti-)de Sitter Lie algebra. This graded manifold comes equipped with a natural presymplectcic structure and the compatible pre-$Q$ structure which is a sum of the Chevalley-Eilenberg differentials of each copy of the Lie algebra and the interaction term. The constraints determining the submanifold are the supergeometrical realisation of the known Deser-van Nieuwenhuizen condition and its descendant. |
| title | Massive bigravity as a presymplectic BV-AKSZ sigma-model |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.13075 |