We construct families of supersymmetric AdS3 × Y7 and AdS3 × Y8 solutions to type IIB string theory and M-theory, respectively. Here Y7 is an S5 fibration over Σ, while Y8 is an S4 fibration over Σg × Σ, where Σg is a Riemann surface of genus g > 1 and Σ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of N D3-branes wrapped on Σ and N M5-branes wrapped on Σg × Σ, respectively. These are holographically dual to d = 2, (0, 2) SCFTs, and we show that the central charge and superconformal R-symmetry of the gravity solutions agree with dual field theory calculations.
We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS 3 solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS 2 solutions of D = 11 supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a twosphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS 3 solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell c-function in the dual field theory, establishing a very general exact result in holography. For the AdS 2 solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS 4 .
We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$$_3$$ 3 solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS$$_2$$ 2 solutions of $$D=11$$ D = 11 supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS$$_3$$ 3 solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell c-function in the dual field theory, establishing a very general exact result in holography. For the AdS$$_2$$ 2 solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS$$_4$$ 4 .
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