Supersymmetric Vacua in N=2 Supergravity

TL;DR

This paper analyzes conditions for N=2 supersymmetric vacua in supergravity, showing that certain symmetries restrict vacua to Minkowski space and exploring the existence of N=2 and N=1 vacua in related theories.

Contribution

It provides a formal analysis of N=2 vacua conditions using the embedding tensor formalism and reveals symmetry constraints on the nature of these vacua.

Findings

N=2 vacua are Minkowski if gauged isometries preserve SU(2) R-symmetry

No AdS backgrounds with full N=2 supersymmetry in certain string compactifications

Existence of N=2 and N=1 vacua for specific gauged isometries

Abstract

We use the embedding tensor formalism to analyse maximally symmetric backgrounds of N=2 gauged supergravities which have the full N=2 supersymmetry. We state the condition for N=2 vacua and discuss some of their general properties. We show that if the gauged isometries leave the SU(2) R-symmetry invariant, then the N=2 vacuum must be Minkowski. This implies that there are no AdS backgrounds with eight unbroken supercharges in the effective N=2 supergravity of six-dimensional SU(3) x SU(3) structure compactifications of type II string theory and M-theory. Combined with previous results on N=1 vacua, we show that there exist N=2 supergravities with a given set of gauged Abelian isometries that have both N=2 and N=1 vacua. We also argue that an analogue of our analysis holds in five and six spacetime dimensions.