Presymplectic AKSZ formulation of Einstein gravity

TL;DR

This paper develops a presymplectic AKSZ framework to encode Einstein gravity's Lagrangian and BV formulation, providing a supergeometric perspective that unifies gauge structures and Hamiltonian formalisms.

Contribution

It introduces a presymplectic AKSZ approach to represent Einstein gravity and its BV formulation, offering a concise and elegant geometric construction.

Findings

Full BV formulation is encoded in the presymplectic AKSZ model.

The approach unifies Lagrangian and Hamiltonian gauge structures.

Provides a supergeometric construction for Einstein gravity.

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.