A New Double-Scaling Limit of N=4 Super Yang-Mills Theory and PP-Wave Strings

TL;DR

This paper introduces a novel double-scaling limit in N=4 super Yang-Mills theory that preserves non-planar diagrams, enabling exact calculations of correlation functions and revealing non-trivial operator mixing and corrections.

Contribution

It demonstrates the existence of a double-scaling limit where non-planar diagrams survive, providing new insights into the gauge/string duality in pp-wave backgrounds.

Findings

Non-planar diagrams survive in the new limit.

Exact two- and three-point functions computed.

Operators exhibit non-planar mixing and anomalous dimension corrections.

Abstract

The metric of a spacetime with a parallel plane (pp)-wave can be obtained in a certain limit of the space AdS^5xS^5. According to the AdS/CFT correspondence, the holographic dual of superstring theory on that background should be the analogous limit of N=4 supersymmetric Yang-Mills theory. In this paper we shall show that, contrary to widespread expectation, non-planar diagrams survive this limiting procedure in the gauge theory. Using matrix model techniques as well as combinatorial reasoning it is demonstrated that a subset of diagrams of arbitrary genus survives and that a non-trivial double scaling limit may be defined. We exactly compute two- and three-point functions of chiral primaries in this limit. We also carefully study certain operators conjectured to correspond to string excitations on the pp-wave background. We find non-planar linear mixing of these proposed operators, requiring their redefinition. Finally, we show that the redefined operators receive non-planar corrections to the planar one-loop anomalous dimension.