| Summary: | Abstract We construct AdS4 × Σ and AdS2 × Σ × Σ g $$ {\Sigma}_{\mathfrak{g}} $$ solutions in F(4) gauged supergravity in six dimensions, where Σ is a two dimensional manifold of non-constant curvature with conical singularities at its two poles, called a spindle, and Σ g $$ {\Sigma}_{\mathfrak{g}} $$ is a constant curvature Riemann surface of genus g $$ \mathfrak{g} $$ . We find that the first solution realizes a “topologically topological twist”, while the second class of solutions gives rise to an “anti twist”. We compute the holographic free energy of the AdS4 × Σ solution and find that it matches the entropy computed by extremizing an entropy functional that is constructed by gluing gravitational blocks. For the AdS2 × Σ × Σ g $$ {\Sigma}_{\mathfrak{g}} $$ solution, we find that the Bekenstein-Hawking entropy is reproduced by extremizing an appropriately defined entropy functional, which leads us to conjecture that this solution is dual to a three dimensional SCFT on a spindle. A class of the AdS2 × Σ × Σ g $$ {\Sigma}_{\mathfrak{g}} $$ solutions can be embedded in four dimensional T 3 gauged supergravity, which is a subtruncation of the six dimensional theory.
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