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

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          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 \(g^4N^2\).

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          Wilson loops in large N field theories

          We propose a method to calculate the expectation values of an operator similar to the Wilson loop in the large N limit of field theories. We consider N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the area of a fundamental string worldsheet in certain supergravity backgrounds. We also consider the case of coincident M-theory fivebranes where one is lead to calculating the area of M-theory two-branes. We briefly discuss the computation for 2+1 dimensional super-Yang-Mills with sixteen supercharges which is non-conformal. In all these cases we calculate the energy of quark-antiquark pair.
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            Author and article information

            Journal
            07 March 2000
            Article
            10.1016/S0550-3213(00)00300-X
            hep-th/0003055
            95c14279-90df-4940-8abe-585f1c550184
            History
            Custom metadata
            ITEP-TH-13/00
            Nucl.Phys. B582 (2000) 155-175
            24 pages, LaTeX, uses feynmp, 12 postscript figures
            hep-th

            High energy & Particle physics
            High energy & Particle physics

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