${\cal N}=(4,4)$ supersymmetric AdS$_3$ solutions in $d=11$

TL;DR

This paper classifies and constructs new ${ m AdS}_3$ solutions in 11-dimensional supergravity with ${ m N}=(4,4)$ supersymmetry, using G-structures and internal manifold decompositions, advancing understanding of supersymmetric backgrounds.

Contribution

It derives conditions for ${ m AdS}_3$ solutions with ${ m N}=(1,1)$ supersymmetry, and explicitly characterizes all ${ m N}=(4,4)$ solutions in 11D supergravity, including new classes and solutions.

Findings

Classified all ${ m N}=(4,4)$ supersymmetric ${ m AdS}_3$ solutions in 11D supergravity.

Identified three classes of solutions based on internal manifold structure.

Constructed new explicit solutions within the derived classes.

Abstract

We derive necessary and sufficient conditions for AdS$_3$ solutions of $d=11$ supergravity to preserve ${\cal N}=(1,1)$ 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 ${\cal N}=(4,4)$ 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 $\mathbb{R}^3$ which can be compactified to $\mathbb{T}^3$. We use our results to construct several new solutions that lie within our derived classes as well as recovering some existing solutions.