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

TL;DR

This paper classifies the most general eleven-dimensional supergravity solutions with $N=2$ supersymmetry that are warped products of AdS$_3$ and an eight-dimensional manifold, revealing conditions for supersymmetry and R-symmetry structures.

Contribution

It provides necessary and sufficient conditions for supersymmetric $N=2$ AdS$_3$ solutions in M-theory using local SU(2) structures and explores new classes of solutions.

Findings

Solutions admit a Killing vector encoding U(1) R-symmetry.

Includes examples with SU(4), G$_2$, and SU(3) structures.

Discusses new Minkowski solutions.

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.