Presymplectic minimal models of local gauge theories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914890148478976 |
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| author | Dneprov, Ivan Grigoriev, Maxim Gritzaenko, Vyacheslav |
| author_facet | Dneprov, Ivan Grigoriev, Maxim Gritzaenko, Vyacheslav |
| contents | We elaborate on the recently proposed notion of a weak presymplectic gauge PDE. It is a $\mathbb{Z}$-graded bundle over the space-time manifold, equipped with a degree $1$ vector field and a compatible graded presymplectic structure. This geometrical data naturally defines a Lagrangian gauge field theory. Moreover, it encodes not only the Lagrangian of the theory but also its full-scale Batalin-Vilkovisky (BV) formulation. In particular, the respective field-antifield space arises as a symplectic quotient of the super-jet bundle of the initial fiber bundle. A remarkable property of this approach is that among the variety of presymplectic gauge PDEs encoding a given gauge theory we can pick a minimal one that usually turns out to be finite-dimensional, and unique in a certain sense. The approach can be considered as an extension of the familiar AKSZ construction to not necessarily topological and diffeomorphism-invariant theories. We present a variety of examples including $p$-forms, chiral Yang-Mills theory, Holst gravity, and conformal gravity. We also explain the explicit relation to the non-BV-BRST version of the formalism, which happens to be closely related to the covariant phase space and the multisymplectic approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_03240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Presymplectic minimal models of local gauge theories Dneprov, Ivan Grigoriev, Maxim Gritzaenko, Vyacheslav High Energy Physics - Theory Mathematical Physics We elaborate on the recently proposed notion of a weak presymplectic gauge PDE. It is a $\mathbb{Z}$-graded bundle over the space-time manifold, equipped with a degree $1$ vector field and a compatible graded presymplectic structure. This geometrical data naturally defines a Lagrangian gauge field theory. Moreover, it encodes not only the Lagrangian of the theory but also its full-scale Batalin-Vilkovisky (BV) formulation. In particular, the respective field-antifield space arises as a symplectic quotient of the super-jet bundle of the initial fiber bundle. A remarkable property of this approach is that among the variety of presymplectic gauge PDEs encoding a given gauge theory we can pick a minimal one that usually turns out to be finite-dimensional, and unique in a certain sense. The approach can be considered as an extension of the familiar AKSZ construction to not necessarily topological and diffeomorphism-invariant theories. We present a variety of examples including $p$-forms, chiral Yang-Mills theory, Holst gravity, and conformal gravity. We also explain the explicit relation to the non-BV-BRST version of the formalism, which happens to be closely related to the covariant phase space and the multisymplectic approaches. |
| title | Presymplectic minimal models of local gauge theories |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2402.03240 |