BMN Correlators by Loop Equations

TL;DR

This paper develops an analytic loop-equation method to evaluate correlators in the BMN limit of N=4 SYM, enabling calculations of higher-genus corrections previously obtained by combinatorics.

Contribution

It introduces a loop-equation based approach for computing expectation values in a Gaussian matrix model relevant to BMN correlators, extending to genus two.

Findings

Reproduces genus one correction to BMN operator anomalous dimensions.

Provides expectation values for genus two corrections.

Offers an analytic alternative to combinatorial methods.

Abstract

In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional Gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction.