Supergravity vacua and lorentzian Lie groups

TL;DR

This paper classifies maximally supersymmetric vacua in six and five-dimensional supergravities, revealing their structure as Lorentzian Lie groups with specific geometric properties, and establishes their correspondence and homogeneous space representations.

Contribution

It provides a complete classification of supergravity vacua as Lorentzian Lie groups with bi-invariant metrics and describes their geometric and algebraic structures.

Findings

Classified (1,0) and (2,0) supergravity vacua in six dimensions.

Established correspondence between (2,0) and (1,0) vacua.

Described five-dimensional vacua as homogeneous spaces from right cosets.

Abstract

We classify maximally supersymmetric backgrounds (vacua) of chiral (1,0) and (2,0) supergravities in six dimensions and, by reduction, also those of the minimal N=2 supergravity in five dimensions. Up to R-symmetry, the (2,0) vacua are in one-to-one correspondence with (1,0) vacua, and these in turn are locally isometric to Lie groups admitting a bi-invariant lorentzian metric with anti-selfdual parallelising torsion, which we classify. We then show that the five-dimensional vacua are homogeneous spaces arising canonically as the spaces of right cosets of spacelike one-parameter subgroups.