Abstract
Any local gauge theory can be represented as an AKSZ sigma model (upon parameterization if necessary). However, for non-topological models in dimension higher than 1 the target space is necessarily infinite-dimensional. The interesting alternative known for some time is to allow for degenerate presymplectic structure in the target space. This leads to a very concise AKSZ-like representation for frame-like Lagrangians of gauge systems. In this work we concentrate on Einstein gravity and show that not only the Lagrangian but also the full-scale Batalin-Vilkovisky (BV) formulation is naturally encoded in the presymplectic AKSZ formulation, giving an elegant supergeometrical construction of BV for Cartan-Weyl action. The same applies to the main structures of the respective Hamiltonian BFV formulation.
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Grigoriev, M., Kotov, A. Presymplectic AKSZ formulation of Einstein gravity. J. High Energ. Phys. 2021, 181 (2021). https://doi.org/10.1007/JHEP09(2021)181
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DOI: https://doi.org/10.1007/JHEP09(2021)181