We construct infinite new classes of supersymmetric solutions of $D=11$ supergravity that are warped products of ${\mathrm{AdS}}_3$ with an eight-dimensional manifold ${\mathcal{M}}_8$ and have nonvanishing four-form flux. In order to be compact, ${\mathcal{M}}_8$ is constructed as an $S^2$ bundle over a six-dimensional manifold $B_6$ which is either Kähler-Einstein or a product of Kähler-Einstein spaces. In the special cases that $B_6$ contains a two-torus, we also obtain new ${\mathrm{AdS}}_3$ solutions of type IIB supergravity, with constant dilaton and only five-form flux. Via the anti-de Sitter (AdS)-conformal field theory (CFT) correspondence the solutions with compact ${\mathcal{M}}_8$ will be dual to two-dimensional conformal field theories with $N=(0,2)$ supersymmetry. Our construction can also describe noncompact geometries and we discuss examples in type IIB which are dual to four-dimensional $N=1$ superconformal theories coupled to stringlike defects.

• Received 27 September 2006

DOI:https://doi.org/10.1103/PhysRevD.74.106007