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

We consider the correlation function of a circular Wilson loop with two local scalar operators at generic four positions a1, a2 in planar N=4 supersymmetric gauge theory. We show that such a correlator is fixed by conformal invariance up to a function F(u,v;λ) of two scalar combinations u,v of a1, a2 coordinates invariant under the conformal transformations preserving the circle as well as the 't Hooft coupling λ. We compute this function at leading orders at weak and strong coupling for some simple choices of local supersymmetric operators. We also check that correlators of an infinite line Wilson loop with local operators are the same as those for the circular loop. © 2013 American Physical Society.