to which the string theory (in the anti-de Sitter background) is dual to are rather poorly understood. This prevents detailed quantitative tests. In this paper we shall formulate similar conjectures based on intersections of branes. The corresponding dual superconformal field theories are two-dimensional and depending on the particular intersection they may be chiral or not. For the intersections we discuss the near-horizon limits correspond to exact conformal field theories. This opens the possibility to perform a detailed and quantitative study of the conjectural relations between string theories on anti-de Sitter backgrounds and superconformal field theories.

The new set of solutions of 11d and 10d supergravities are of the form $adS_k \xx S^l \xx S^m \xx E^n$, with $k, l, m=2, 3$ and $n$ is such that the dimensions sum up to $10$ or $11$ depending on the solution. These solutions are actually exact solutions of string theory, i.e. there is a conformal field theory (CFT) associated to them. For $S^3$ this is an $SO(3)$ WZW model and for $adS_3$ an $SL(2, R)$ WZW model. The one associated with $S^2$ [@GPSmonopole] follows from the fact that $S^3$ is a $U(1)$ bundle over $S^2$ (Hopf fibration). The CFT associated with $adS_2$ follows 