N = (2, 0) AdS3 solutions of M-theory

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), G2 and SU(3) structures, and discuss new classes of Minkowski solutions.

AdS3 vacua realising $$ \mathfrak{osp} $$(n|2) superconformal symmetry

“…A free field relation was presented in [21] (see also [22]) in terms of a free scalar, n real fermions, and an SO(n) current algebra of level k − 1. There are in fact many examples of AdS 3 vacua realising osp(n|2) for n = 1, 2 as these are the unique ways to realise (1, 0) and (2, 0) superconformal symmetries -see for instance respectively [23][24][25][26][27][28][29][30][31][32] and [11,[33][34][35][36][37][38][39][40][41][42][43] . Similarly n = 3 is unique for N = (3,0), examples are more sparse [44][45][46], but this is likely not a reflection of their actual rarity.…”