Correlators Of Operators with a Large R-charge

TL;DR

This paper investigates correlation functions of high-dimension operators in N=4 super Yang-Mills theory, revealing resummation of non-planar corrections, a modified 1/(M+N) expansion, and connections to giant graviton backgrounds and BMN sectors.

Contribution

It introduces a resummation method for non-planar diagrams at large R-charge and establishes exact relationships between amplitudes in different giant graviton backgrounds.

Findings

Resummation of non-planar corrections in high R-charge correlators.

Replacement of 1/N expansion with 1/(M+N) expansion in specific backgrounds.

Evidence for decoupled BMN-like sectors in intersecting giant graviton systems.

Abstract

Correlation functions of operators with a conformal dimension of O(N^2) are not well approximated by the planar limit. The non-planar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. In this article we show how these loop corrections can be resummed. As a typical example of our results, in the half-BPS background of M maximal giant gravitons we find the usual 1/N expansion is replaced by a 1/(M+N) expansion. Further, we find that there is a simple exact relationship between amplitudes computed in the trivial background and amplitudes computed in the background of M maximal giant gravitons. Finally, we also find strong evidence for the BMN-type sectors suggested in arXiv:0801.4457. The decoupling limit of arXiv:0801.4457 captures the decoupled low energy world volume theory of the intersecting giant graviton system and this theory is weakly coupled even when the original N=4 super Yang-Mills theory is strongly coupled.