On the supersymmetry invariance of flat supergravity with boundary

TL;DR

This paper investigates how to maintain supersymmetry invariance in four-dimensional flat supergravity with boundaries by adding boundary terms and gauge fields, and constructs an enlarged model that reduces to flat supergravity in a specific limit.

Contribution

It introduces a geometric method to preserve supersymmetry invariance in flat supergravity with boundaries by adding boundary terms and gauge fields without altering the bulk Lagrangian.

Findings

Boundary terms are necessary for supersymmetry invariance.

Additional gauge fields at the boundary preserve invariance.

An enlarged supergravity model reduces to flat supergravity in the limit.

Abstract

The supersymmetry invariance of flat supergravity (i.e., supergravity in the absence of any internal scale in the Lagrangian) in four dimensions on a manifold with non-trivial boundary is explored. Using a geometric approach we find that the supersymmetry invariance of the Lagrangian requires to add appropriate boundary terms. This is achieved by considering additional gauge fields to the boundary without modifying the bulk Lagrangian. We also construct an enlarged supergravity model from which, in the vanishing cosmological constant limit, flat supergravity with a non-trivial boundary emerges properly.