We study non planar corrections to the spectrum of operators in the ${ \mathcal N}=2$ supersymmetric Yang Mills theory which are dual to string states in the maximally supersymmetric pp-wave background with a { \em compact} light-cone direction. The existence of a positive definite discrete light-cone momentum greatly simplifies the operator mixing problem. We give some examples where the contribution of all orders in non-planar diagrams can be found analytically. On the string theory side this corresponds to finding the spectrum of a string state to all orders in string loop corrections.
Categories: hep-th