On strong-coupling correlation functions of circular Wilson loops and local operators

TL;DR

This paper investigates strong-coupling three-point functions involving Wilson loops and local operators in N=4 super Yang-Mills, using semiclassical string methods to compute correlators with elliptic function integrals.

Contribution

It provides a detailed analysis of correlators involving concentric Wilson loops and light operators, extending to cases with angular momentum and heavy operators at strong coupling.

Findings

Analytic expressions for correlators involving Wilson loops and dilaton operators.

Extension to cases with non-zero angular momentum J in S^5.

Discussion of limits where Wilson loops are replaced by heavy operators.

Abstract

Motivated by the problem of understanding 3-point correlation functions of gauge-invariant operators in N =4 super Yang-Mills theory we consider correlators involving Wilson loops and a "light" operator with fixed quantum numbers. At leading order in the strong coupling expansion such correlators are given by the "light" vertex operator evaluated on a semiclassical string world surface ending on the corresponding loops at the boundary of AdS_5 x S^5. We study in detail the example of a correlator of two concentric circular Wilson loops and a dilaton vertex operator. The resulting expression is given by an integral of combinations of elliptic functions and can be computed analytically in some special limits. We also consider a generalization of the minimal surface ending on two circles to the case of non-zero angular momentum J in S^5 and discuss a special limit when one of the Wilson loops is effectively replaced by a "heavy" operator with charge J.