$N=(2,0)$ AdS${}_3$ Solutions of M-theory

Abstract

We consider the most general solutions of eleven-dimensional supergravity preserving $N=2$ supersymmetry whose metrics are warped products of three-dimensional anti-de Sitter space with an eight-dimensional manifold, focusing on those realising (2,0) superconformal symmetry. We give a set of necessary and sufficient conditions for a solution to be supersymmetric, which can be phrased, in the general case, in terms of a local SU(2) structure and its intrinsic torsion. We show that these supergravity backgrounds always admit a nowhere-vanishing Killing vector field that preserves the solution and encodes the U(1) R-symmetry of the dual field theory. We illustrate our results with examples which have appeared in the literature, including those with SU(4), G${}_2$ and SU(3) structures, and discuss new classes of Minkowski solutions.

40 pages plus appendices; submission includes two Mathematica notebooks; v2: references added; v3: version accepted for publication

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Cited by in corpus (2)

• Equivariant localization for AdS/CFT
• Localizing Wrapped M5-branes and Gravitational Blocks