Presymplectic AKSZ formulation of Einstein gravity

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. We show that a full-scale Batalin-Vilkovisky (BV) and Hamiltonian BRST formulations are naturally encoded in the presymplectic AKSZ formulation. In particular, this gives an elegant supergeometrical construction of BV for Cartan-Weyl action in the case of gravity. Further generalisations lead to a Lagrangian version of the invariant geometric formalism for local gauge field theories. Идентификатор конференции в Zoom: 828 5783 2979. Код доступа можно узнать у организаторов семинара.