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

A bstract We derive necessary and sufficient conditions for AdS 3 solutions of d = 11 supergravity to preserve $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (1, 1) supersymmetry in terms of G-structures. Such solutions necessarily support an SU(3)-structure on the internal 8-manifold M 8 , in terms of which we phrase the conditions for supersymmetry preservation. We use this to derive the local form of all $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (4, 4) supersymmetric AdS 3 solutions in d = 11, for which M 8 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 M 5 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 M 5 maintains its 3-sphere, one where this blows up to ℝ 3 which can be compactified to 𝕋 3 . We use our results to construct several new solutions that lie within our derived classes as well as recovering some existing solutions.