Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity

TL;DR

This paper explores rigid supersymmetric backgrounds in minimal N=1 off-shell supergravity, constructing various solutions including AdS_4 and new Euclidean backgrounds like squashed spheres and flat space variants.

Contribution

It systematically constructs all rigid supersymmetry backgrounds with hypersurface orthogonal Killing vectors in both Lorentzian and Euclidean signatures, revealing new Euclidean solutions.

Findings

AdS_4 admits rigid supersymmetry in both formulations

New Euclidean backgrounds include squashed four-spheres

Half-BPS flat space in Euclidean supergravity

Abstract

We discuss various aspects of rigid supersymmetry within minimal N=1 off-shell supergravity using the old and new minimal formulations both in Lorentzian and Euclidean signatures. In particular, we construct all rigid supersymmetry backgrounds with a hypersurface orthogonal Killing vector. In the Lorentzian signature we show that AdS_4 provides a rigid supersymmetric background in both formulations albeit with different amounts of preserved supersymmetry. In the Euclidean signature we find new backgrounds of the old-minimal supergravity, including squashed four-spheres and a half-BPS version of flat space.