Charges of supergravity

TL;DR

This paper analyzes conserved charges in $ ext{AdS}_4$ $ ext{N}=1$ supergravity using a covariant phase space approach, revealing the structure of boundary charges and their algebra.

Contribution

It derives explicit expressions for bulk and boundary charges in supergravity formulated as a constrained BF theory, clarifying their algebraic structure.

Findings

Boundary charge algebra reproduces the superalgebra.

Translational charges vanish on-shell due to super-torsion constraints.

Lorentz and supersymmetry charges are the non-trivial generators.

Abstract

We study conserved charges of $\mathcal{N}=1$ supergravity formulated as a constrained BF theory based on the $\OSp(1|4)$ superalgebra. Using the covariant phase space formalism, we derive bulk and boundary contributions to the symplectic structure and construct charges associated with Lorentz transformations, supersymmetry, translations, and diffeomorphisms. We show that the algebra of boundary charges reproduces the expected superalgebra, while translational charges vanish on-shell due to the super-torsion constraint, leaving Lorentz and supersymmetry as the non-trivial generators.