Dario Martelli, Achilleas Passias, James Sparks
We show that a given conformal boundary can have a rich and intricate space of supersymmetric supergravity solutions filling it, focusing on the case where this conformal boundary is a biaxially squashed Lens space. For example, the squashed three-sphere has a 1/4 BPS Taub-NUT-AdS filling, with topology R^4, but also three inequivalent supersymmetric Taub-Bolt-AdS solutions with non-trivial topology. We show that the Taub-NUT-AdS solutions generically lift to solutions of M-theory, and correspondingly that the gravitational free energy then agrees with the large N limit of the dual field theory free energy, obtained from the localized partition function of a class of N=2 Chern-Simons-matter theories. However, the solutions of Taub-Bolt-AdS type only lift to M-theory for appropriate classes of internal manifold, meaning that only in certain cases do the three-dimensional N=2 field theories exhibit the complicated phase structure that we uncover on the gravity side.
View original:
http://arxiv.org/abs/1212.4618
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