Massive bigravity as a presymplectic BV-AKSZ sigma-model

TL;DR

This paper develops a presymplectic BV-AKSZ sigma model framework to encode ghost-free massive bigravity theory, utilizing graded geometry and Lie algebra structures to extend the theory in a finite-dimensional setting.

Contribution

It introduces a novel presymplectic BV-AKSZ sigma model formulation of massive bigravity using graded geometry and Lie algebra techniques, providing a new geometric perspective.

Findings

Constructed a finite-dimensional graded geometric model for bigravity.

Encoded the bigravity action and BV extension within the model.

Revealed geometric structures underlying the ghost-free bigravity theory.

Abstract

We propose a presymplectic BV-AKSZ sigma model encoding the ghost-free massive bigravity theory action as well as its Batalin-Vilkovisky extension in terms of the finite-dimensional graded geometry of the target space. A characteristic feature of the construction is that the target space is realised as a quasi-regular submanifold of a linear graded manifold which, in turn, is a direct product of two copies of the shifted Poincar\'e or (anti-)de Sitter Lie algebra. This graded manifold comes equipped with a natural presymplectcic structure and the compatible pre-$Q$ structure which is a sum of the Chevalley-Eilenberg differentials of each copy of the Lie algebra and the interaction term. The constraints determining the submanifold are the supergeometrical realisation of the known Deser-van Nieuwenhuizen condition and its descendant.