The Reduced Phase Space of $N=1, D=4$ Supergravity in the BV-BFV formalism

TL;DR

This paper explicitly constructs the reduced phase space of four-dimensional N=1 supergravity using the BV-BFV formalism, clarifying boundary constraints and their relation to bulk quantization methods.

Contribution

It provides an explicit description of the boundary constraints and the BFV formulation for N=1 supergravity in four dimensions within the BV-BFV framework.

Findings

Explicit boundary first-class constraints derived

BFV description of supergravity obtained

Relation between boundary and bulk BV formalisms established

Abstract

This paper describes the reduced phase space of $N=1$, $D=4$ supergravity in the fully off-shell Palatini--Cartan formalism. This is achieved through the KT construction, allowing an explicit description of first-class constraints on the boundary. The corresponding BFV description is obtained, and its relation with the BV one in the bulk is described by employing the BV pushforward in the particular example of a cylindrical spacetime.