Partition functions on 3d circle bundles and their gravity duals

Abstract

Abstract The partition function of a three-dimensional $$ \mathcal{N}=2 $$ N = 2 theory on the manifold ℳ g,p , an S 1 bundle of degree p over a closed Riemann surface Σ g , was recently computed via supersymmetric localization. In this paper, we compute these partition functions at large N in a class of quiver gauge theories with holographic M-theory duals. We provide the supergravity bulk dual having as conformal boundary such three-dimensional circle bundles. These configurations are solutions to $$ \mathcal{N}=2 $$ N = 2 minimal gauged supergravity and pertain to the class of Taub-NUT-AdS and Taub-Bolt-AdS preserving 1/4 of the supersymmetries. We discuss the conditions for the uplift of these solutions to M-theory, and compute the on-shell action via holographic renormalization. We show that the uplift condition and on-shell action for the Bolt solutions are correctly reproduced by the large N limit of the partition function of the dual superconformal field theory. In particular, the Σ g  × S 1 = ℳ g,0 partition function, which was recently shown to match the entropy of AdS4 black holes, and the S 3 ≅ ℳ0,1 free energy, occur as special cases of our formalism, and we comment on relations between them.