NUTs and Bolts: free energy via susy localization

The partition function of three-dimensional N=2 SCFTs on circle bundles of closed Riemann surfaces \Sigma_g was recently computed via supersymmetric localization. In this talk I will describe supergravity solutions having as conformal boundary such circle bundle. These configurations are solutions to N=2 minimal gauged supergravity in 4d and pertain to the class of AdS-Taub-NUT and AdS-Taub-Bolt preserving 1/4 of the supersymmetries. I will discuss the conditions for the uplift of these solutions to M-theory and I provide the expression for the on-shell action of the Bolt solutions, computed via holographic renormalization. I will show that, when the uplift condition is satisfied, the Bolt free energy matches with the large N limit of the partition function of the corresponding dual field theory. I will finally comment on possible subtleties that arise in our framework when a given boundary geometry admits multiple bulk fillings.

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Friday, May 10, 2019 - 14:30 to 16:00
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