The Duality between IIB string theory on PP wave and N = 4 SYM: a status report

The aim of this report is to give an overview of the duality between type IIB string theory on the maximally supersymmetric PP-wave and the BMN sector of the N = 4 super-Yang-Mills theory. The general features of the string and the field theory descriptions are reviewed, but the main focus of this report is on the comparison between the two sides of the duality. In particular, it is first explained how free 1113 strings emerge on the gauge theory side and then the generalizations of this relation to the full interacting theory are considered. A 'historical' approach is taken and various proposals presented in the literature are described.