Correlation function of circular Wilson loop with two local operators and conformal invariance

TL;DR

This paper analyzes the correlation function between a circular Wilson loop and two local operators in N=4 supersymmetric gauge theory, demonstrating conformal invariance constraints and computing the function at weak and strong coupling.

Contribution

It provides the first explicit computation of the correlation function's conformal invariant part at both weak and strong coupling in this setup.

Findings

Correlation function fixed by conformal invariance up to a coupling-dependent function

Explicit weak and strong coupling calculations for BPS operators

Equivalence of correlators for circular and infinite line Wilson loops

Abstract

We consider the correlation function of a circular Wilson loop with two local scalar operators at generic 4-positions in planar N=4 supersymmetric gauge theory. We show that such correlator is fixed by conformal invariance up to a function of 't Hooft coupling and two scalar combinations of the positions invariant under the conformal transformations preserving the circle. We compute this function at leading orders at weak and strong coupling for some simple choices of local BPS operators. We also check that correlators of an infinite line Wilson loop with local operators are the same as those for the circular loop.