Supersymmetric AdS$$_2\times \Sigma _2$$ 2×Σ2 solutions from tri-sasakian truncation

Abstract

Abstract A class of $$\mathrm{AdS}_2\times \Sigma _2$$ AdS2×Σ2 , with $$\Sigma _2$$ Σ2 being a two-sphere or a hyperbolic space, solutions within four-dimensional $$N=4$$ N=4 gauged supergravity coupled to three-vector multiplets with dyonic gauging is identified. The gauged supergravity has a non-semisimple $$SO(3)\ltimes ({\mathbf {T}}^3,\hat{{\mathbf {T}}}^3)$$ SO(3)⋉(T3,T^3) gauge group and can be obtained from a consistent truncation of 11-dimensional supergravity on a tri-sasakian manifold. The maximally symmetric vacua contain $$\mathrm{AdS}_4$$ AdS4 geometries with $$N=1,3$$ N=1,3 supersymmetry corresponding to $$N=1$$ N=1 and $$N=3$$ N=3 superconformal field theories (SCFTs) in three dimensions. We find supersymmetric solutions of the form $$\mathrm{AdS}_2\times \Sigma _2$$ AdS2×Σ2 preserving two supercharges. These solutions describe twisted compactifications of the dual $$N=1$$ N=1 and $$N=3$$ N=3 SCFTs and should arise as near horizon geometries of dyonic black holes in asymptotically $$\mathrm{AdS}_4$$ AdS4 space-time. Most solutions have hyperbolic horizons although some of them exhibit spherical horizons. These provide a new class of $$\mathrm{AdS}_2\times \Sigma _2$$ AdS2×Σ2 geometries with known M-theory origin.