Supersymmetric backgrounds of M-theory and AdS4/CFT3 correspondence
We analyse the most general N = 2 supersymmetric solutions of d = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a sevendimensional Riemannian manifold Y7. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structure on Y7. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ordinary differential equation. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS4×S7 solution with non-trivial four-form flux. Furthermore, we study supersymmetric asymptotically locally AdS4 solutions of N = 2 gauged supergravity which via the AdS4/CFT3 correspondence are dual to supersymmetric gauge theories on deformed 3-spheres with SU(2)×U(1) symmetry and a non-trivial background gauge field. These solutions lift to solutions of M-theory and we show that the gravitational free energy 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. In this context, we present a complete class of supersymmetric backgrounds of N = 2 gauged supergravity whose conformal boundary is a biaxially squashed Lens space S3/Zp. Generically we find that the latter admits Taub-NUT-AdS fillings, with topology R4/Zp, as well as smooth Taub-Bolt-AdS fillings with non-trivial topology.
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