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Abstract |
I will review recent progress in computing the partition function of 3d SCFTs on closed manifolds via supersymmetric localization. I will then provide examples of dual supergravity solutions having as conformal boundary such manifolds. I will start with the simple case where the dual geometry is a static AdS black hole, showing how the microstate counting in the dual field theory accounts for black hole entropy. Then I will describe solutions having as boundary a circle bundle over closed 2d Riemann surface (AdS-Taub-NUT and AdS-Taub-Bolt) and I will show the matching of their on-shell action with the large N limit of the partition function of the dual CFT. I will finally discuss some recent results for a third and more challenging example, which involves the refinement by angular momentum. |
