Abstract
We construct supersymmetric solutions of theories of gauged mathcal{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.
Highlights
Case, one can use supersymmetry to derive very powerful solution-generating techniques
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
In this paper we work in the framework of the 5-dimensional theories (N = 1, d = 5 supergravity coupled to vector multiplets) and we are going to consider the first of these possibilities: an Abelian U(1)R gauging that will produce a scalar potential with AdS vacua and, at the same time, an independent non-Abelian gauging of a subgroup of the isometry group of the scalar manifold
Summary
We describe the two theories we are going to work with They are two different models of gauged N = 1, d = 5 supergravity coupled to vector supermultiplets with gauge groups consisting in a U(1) factor associated to a Fayet-Iliopopulos term and second, non-Abelian factor (SU(2) and SU(3)) associated to the gauging of the isometry group of the (Real Special) scalar manifold. Gauging the full R-symmetry group, involves a deformation of a SEYM model in which new couplings to the fermions are introduced in the action, as well as fermion shifts in the supersymmetry transformation rules and a non-vanishing scalar potential (see eq (2.12) below). The latter occurs in the bosonic action.
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