Classification of maximally supersymmetric backgrounds in supergravity theories

TL;DR

This paper classifies all maximally supersymmetric backgrounds in supergravity theories across dimensions, establishing conditions for solutions with non-trivial fluxes and confirming the completeness of known solutions.

Contribution

It provides a comprehensive criterion for existence of solutions with fluxes and shows these solutions match those of ungauged theories, confirming the exhaustiveness of known solutions.

Findings

Maximally supersymmetric solutions are either Minkowski or anti-de Sitter for zero flux.

A simple criterion for solutions with non-trivial fluxes is derived.

All such solutions are shown to be already known from ungauged theories.

Abstract

We study maximally supersymmetric solutions of all gauged or deformed supergravity theories in $D \ge 3$ space-time dimensions. For vanishing background fluxes the space-time background has to be either Minkowski or anti-de Sitter. We derive a simple criterion for the existence of solutions with non-trivial fluxes and determine all supergravities that satisfy it. We show that their solutions coincide with those of the corresponding ungauged theories and conclude that the known list of maximally supersymmetric solutions is exhaustive.