The Duality between IIB String Theory on PP-wave and N=4 SYM: a Status Report

TL;DR

This report reviews the duality between IIB string theory on PP-wave backgrounds and the BMN sector of N=4 SYM, focusing on the emergence of free strings and their interactions within the gauge theory framework.

Contribution

It provides a comprehensive overview of the duality, including historical context, string and field theory descriptions, and the transition from free to interacting theories.

Findings

Free IIB strings emerge in the gauge theory side.

Generalizations to interacting theories are discussed.

Various proposals in the literature are reviewed.

Abstract

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 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 IIB strings emerge on the gauge theory side and then the generalizations of this relation to the full interacting theory are considered. An ``historical'' approach is taken and the various proposals presented in the literature are described.