3D Supergravity in the Batalin-Vilkovisky Formalism
Alberto S. Cattaneo, Nima Moshayedi, Alberto Smailovic Funcasta
TL;DR
The paper addresses constructing a BV formulation of three-dimensional supergravity by leveraging the established equivalence between Palatini–Cartan gravity and BF theory in 3D. By embedding spin-$\frac{3}{2}$ fields into a BF theory and applying the AKSZ construction, the authors obtain a BV action and cohomological vector field that encode both diffeomorphism and local supersymmetry ghosts. A key contribution is the explicit, minimal extension of the BF transformation to BF$\Phi$ and GR$\Phi$, yielding a BV theory whose on-shell limit reproduces classical 3D supergravity and provides concrete formulas for the BV action and symmetry transformations. The results offer a streamlined BV description with potential applications to BV–BFV boundary structures and quantization in the presence of boundaries, advancing the understanding of gravity coupled to matter in lower dimensions.
Abstract
Three-dimensional supergravity in the Batalin-Vilkovisky formalism is constructed by showing that the theory including the Rarita-Schwinger term is equivalent to an AKSZ theory.