Notes on superconformai Chern-Simons-Matter theories

The three dimensional N = 2 supersymmetric Chern-Simons theory coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformai theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large N limit, and compute the two-loop anomalous dimension of certain long operators. Our result suggests that various N = 2 U(N) Chern-Simons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4 which are not yet constructed. © SISSA 2007.