Correlation function of null polygonal Wilson loops with local operators

TL;DR

This paper computes the correlation function of null polygonal Wilson loops with local operators in N=4 super Yang-Mills theory at both weak and strong coupling, revealing its dependence on conformal ratios and exploring its behavior for various polygon sizes.

Contribution

It provides the first explicit calculations of the correlator function F(,,,,,,,,) at leading order in both regimes, including for polygons with more than four edges.

Findings

Explicit form of F(,,,) at weak coupling

Explicit form of F(,,,) at strong coupling

Connection to correlators of local operators at null-separated points

Abstract

We consider the correlator <W_n O(x)> of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or the chiral primary scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n-11 conformal ratios. The first non-trivial case is n=4 when F depends on just one conformal ratio \zeta. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the `t Hooft coupling \lambda. We compute F(\zeta,\lambda) at leading order in both the strong coupling regime (using semiclassical AdS5 x S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.