The supersymmetric NUTs and bolts of holography

TL;DR

This paper explores the rich space of supersymmetric solutions in supergravity filling a biaxially squashed Lens space boundary, linking gravitational solutions to dual field theories via holography.

Contribution

It characterizes Taub-NUT-AdS and Taub-Bolt-AdS solutions with complex topologies and their lift to M-theory, connecting these solutions to dual N=2 field theories.

Findings

Taub-NUT-AdS solutions always lift to M-theory.

Gravitational free energy matches large N field theory predictions.

Taub-Bolt-AdS solutions lift only for specific internal manifolds.

Abstract

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. Generically we find that the biaxially squashed Lens space S^3/Z_p admits Taub-NUT-AdS fillings, with topology R^4/Z_p, as well as smooth Taub-Bolt-AdS fillings with non-trivial topology. We show that the Taub-NUT-AdS solutions always 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 these solutions exist only for corresponding classes of three-dimensional N=2 field theories.