Exact anomalous dimensions of {\cal N}=4 Yang-Mills operators with large R charge

TL;DR

This paper calculates the exact anomalous dimensions of certain operators in { m N}=4 Yang-Mills theory with large R charge, confirming a key aspect of the gauge/string duality in a specific limit.

Contribution

It provides an all-orders perturbative calculation of anomalous dimensions for large R charge operators, verifying their finiteness and supporting the gauge/string duality conjecture.

Findings

Anomalous dimensions are finite in the large R charge limit.

The calculation is valid to all orders in planar perturbation theory.

Supports the duality between { m N}=4 Yang-Mills and string theory in a pp-wave background.

Abstract

In a {\cal N}=1 superspace formulation of {\cal N}=4 Yang-Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J \to \infty keeping g^2 N/J^2 finite, to all orders of perturbation theory in the planar limit. Our result proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of {\cal N}=4 Yang-Mills theory with large R charge J and string theory in a pp-wave background.