Supersymmetric solutions of the cosmological, gauged, ℂ magic model

Abstract

We construct supersymmetric solutions of theories of gauged N = 1, d = 5 supergravity coupled to vector multiplets with a U(1)R Abelian (Fayet-Iliopoulos) gauging and an independent SU(2) gauging associated to an SU(2) isometry group of the Real Special scalar manifold. These theories provide minimal supersymmetrizations of 5-dimensional SU(2) Einstein-Yang-Mills theories with negative cosmological constant. We consider a minimal model with these gauge groups and the “magic model” based on the Jordan algebra J3ℂ with gauge group SU(3) × U(1)R, which is a consistent truncation of maximal SO(6)-gauged supergravity in d = 5 and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual SU(2) instantons, some of which asymptote to AdS5 and some of which are very small, supersymmetric, deformations of AdS5. We also show how some of those solutions can be embedded in Romans’ SU(2) × U(1)-gauged half-maximal supergravity, which was obtained by Lu, Pope and Tran by compactification of the Type IIB Superstring effective action. This provides another way of uplifting those solutions to 10 dimensions.