Partition functions on 3d circle bundles and their gravity duals

The partition function of a three-dimensional N = 2 theory on the manifold M-g,M-p an S-1 bundle of degree p over a closed Riemann surface Sigma(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 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 Sigma(g) x S-1 congruent to M-g,M-0 partition function, which was recently shown to match the entropy of AdS(4) black holes, and the S-3 congruent to M-0,M-1 free energy, occur as special cases of our formalism, and we comment on relations between them.