Exact 1/N expansion of Wilson loop correlators in N=4 Super-Yang-Mills theory

Supersymmetric circular Wilson loops in N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/ N and to all orders in the 't Hooft coupling lambda was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in lambda, but also to all orders in lambda by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/ N series, which can probably be generalized to higher-point correlators.

Automated summary

This paper discusses supersymmetric circular Wilson loops in N = 4 Super-Yang-Mills theory, deriving results on generating functions and connected correlators of Wilson loops. New results on the expectation value of circular Wilson loops are obtained, and a method for calculating series expansions based on the Drukker and Gross approach is presented.