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

Abstract

Motivated by the problem of understanding 3-point correlation functions of gauge-invariant operators in 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 AdS5 × S5. 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 S5 and discuss a special limit when one of the Wilson loops is effectively replaced by a ‘heavy’ operator with charge J.