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

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

2000-03-08

arxiv.org/abs/hep-th/0003055v1

Nucl.Phys. B582 (2000) 155-175

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, LaTeX, uses feynmp, 12 postscript figures

Scientific paper

10.1016/S0550-3213(00)00300-X

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, $\sim\exp((constant)\sqrt{g^2N})$. 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 $g^4N^2$.

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