Distinguishing Off-Shell Supergravities With On-Shell Physics

TL;DR

This paper demonstrates that different off-shell supergravity formulations can be distinguished by their on-shell physical implications, particularly through supersymmetric compactifications and boundary modes.

Contribution

It provides a method to differentiate off-shell supergravity formulations based on on-shell physics, focusing on new minimal versus old minimal formulations.

Findings

Certain 3-manifolds admit supersymmetric compactifications only in the new minimal formulation.

Singleton modes appear in the new minimal formulation but not in others.

The distinction impacts the understanding of supersymmetric backgrounds in supergravity.

Abstract

We show that it is possible to distinguish between different off-shell completions of supergravity at the on-shell level. We focus on the comparison of the ``new minimal'' formulation of off-shell four-dimensional N=1 supergravity with the ``old minimal'' formulation. We show that there are 3-manifolds which admit supersymmetric compactifications in the new-minimal formulation but which do not admit supersymmetric compactifications in other formulations. Moreover, on manifolds with boundary the new-minimal formulation admits ``singleton modes'' which are absent in other formulations.