Maximally supersymmetric solutions of $R^2$ supergravity

TL;DR

This paper classifies all maximally supersymmetric solutions in four-dimensional off-shell N=1 supergravity, revealing that three specific spacetimes are solutions of no-scale R^2 supergravity, and provides a new derivation of these backgrounds.

Contribution

It identifies and demonstrates that three less-known maximally supersymmetric backgrounds are solutions of no-scale R^2 supergravity and offers a simplified derivation method.

Findings

Three additional superspaces are solutions of no-scale R^2 supergravity.

Minkowski and AdS superspaces are known solutions of supergravity.

A new, simpler derivation of maximally supersymmetric backgrounds is provided.

Abstract

There are five maximally supersymmetric backgrounds in four-dimensional off-shell N=1 supergravity, two of which are well known: Minkowski superspace M^{4|4} and anti-de Sitter superspace AdS^{4|4}. The three remaining supermanifolds support spacetimes of different topology, which are: R x S^3, AdS_3 x R, and a supersymmetric plane wave isometric to the Nappi-Witten group. As is well known, the Minkowski and anti-de Sitter superspaces are solutions of the Poincar\'e and anti-de Sitter supergravity theories, respectively. Here we demonstrate that the other three superspaces are solutions of no-scale $R^2$ supergravity. We also present a new (probably the simplest) derivation of the maximally supersymmetric backgrounds of off-shell N=1 supergravity.