Wilson Loops in N=4 Supersymmetric Yang--Mills Theory

TL;DR

This paper computes Wilson loop expectation values in N=4 SYM, showing agreement with AdS/CFT predictions at strong coupling for specific loops and suggesting the ladder diagram sum may be exact.

Contribution

It analytically sums ladder diagrams for circular loops and conjectures their exactness, connecting perturbative results with supergravity predictions.

Findings

Ladder diagram sum matches strong coupling AdS/CFT results.

Analytic expression obtained for circular loop at all couplings.

Leading corrections to ladder diagrams cancel in four dimensions.

Abstract

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $<W>\sim\exp((constant)\sqrt{g^2N})$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $\sqrt{g^2N}$ also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order $g^4N^2$.