\( \mathcal{N} \) = (4, 4) supersymmetric AdS3 solutions in d = 11

Abstract

We derive necessary and sufficient conditions for AdS₃ solutions of d = 11 supergravity to preserve \( \mathcal{N} \) = (1, 1) supersymmetry in terms of G-structures. Such solutions necessarily support an SU(3)-structure on the internal 8-manifold M₈, in terms of which we phrase the conditions for supersymmetry preservation. We use this to derive the local form of all \( \mathcal{N} \) = (4, 4) supersymmetric AdS₃ solutions in d = 11, for which M₈ decomposes as a foliation of a 3-sphere over a 5 dimensional base. There are 3 independent classes, 2 of which preserve the small superconformal algebra and one preserving its large counterpart for which M₅ contains a second 3-sphere. We show that for each solution with large (4, 4) supersymmetry there are two corresponding solutions with small (4, 4), one for which M₅ maintains its 3-sphere, one where this blows up to ℝ³ which can be compactified to 𝕋³. We use our results to construct several new solutions that lie within our derived classes as well as recovering some existing solutions.