Supersymmetric solutions of the cosmological, gauged, C magic model

We construct supersymmetric solutions of theories of gauged $\mathcal{N}=1,d=5$ supergravity coupled to vector multiplets with a $\mathrm{U}(1{)}_{\mathrm{R}}$ Abelian (Fayet-Iliopoulos) gauging and an independent SU$(2)$ gauging associated to an $\mathrm{S}\mathrm{U}(2)$ 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 ${\mathbf{J}}_{\mathbf{3}}^{\mathbb{C}}$ with gauge group $\mathrm{S}\mathrm{U}(3)\times \mathrm{U}(1{)}_{\mathrm{R}}$, which is a consistent truncation of maximal $\mathrm{S}\mathrm{O}(6)$-gauged supergravity in $d=5$ and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual $\mathrm{S}\mathrm{U}(2)$ instantons, some of which asymptote to AdS${}_5$ and some of which are very small, supersymmetric, deformations of AdS${}_5$. We also show how some of those solutions can be embedded in Romans’ $\mathrm{S}\mathrm{U}(2)\times \mathrm{U}(1)$-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.