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

Abstract

Abstract We derive necessary and sufficient conditions for AdS3 solutions of d = 11 supergravity to preserve N $$ \mathcal{N} $$ = (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 N $$ \mathcal{N} $$ = (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.

Keywords

• Extended Supersymmetry
• Flux Compactifications
• AdS-CFT Correspondence