Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models

TL;DR

This paper proposes a novel method to compute correlation functions of certain BPS Wilson loops and local operators in N=4 Super Yang-Mills theory using 2d Yang-Mills and matrix models, with checks against string theory.

Contribution

It introduces a new correspondence between 4d N=4 SYM observables and 2d YM, deriving a two-matrix model for these correlators and validating it through perturbative and strong coupling analyses.

Findings

Two-matrix model reproduces correlators of Wilson loops and local operators.

Strong coupling limit matches string theory calculations.

Perturbative checks support the 2d YM and matrix model correspondence.

Abstract

We propose that, in N=4 Super Yang-Mills theory, correlation functions of certain 1/8 BPS Wilson loops and local operators inserted on a S^2 in space-time may be computed in terms of analogous observables in the "zero-instanton" sector of 2d Yang-Mills theory. The Wilson loops are mapped to the standard Wilson loops of the 2d theory, as recently conjectured, while the local operators are mapped to powers of the 2d field strength. We give several perturbative checks of the correspondence, and derive from 2d Yang-Mills a two-matrix model for the correlator of a local operator and a Wilson loop of arbitrary shape. We show that the strong coupling planar limit of the two-matrix model precisely agrees with a string theory calculation in AdS_5 x S^5.