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arXiv · 2008.11690

Presymplectic AKSZ formulation of Einstein gravity

Maxim Grigoriev·Alexei Kotov
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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 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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Maxim Grigoriev, Alexei Kotov. 2020-08-26. Presymplectic AKSZ formulation of Einstein gravity. https://doi.org/10.1007/jhep09(2021)181

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