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

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

24 pages, LaTeX, uses feynmp, 12 postscript figures

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• Navigating Collinear Superspace
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops
• 1- Brane Sources for the Lightcone Worldsheet: Q-branion - {\bar Q}-branion Scattering to One Loop
• Dilogarithm ladders from Wilson loops
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Null Zig-Zag Wilson Loops in N=4 SYM
• Asymptotic behavior of large polygonal Wilson loops in confining gauge theories
• Circumnavigating Collinear Superspace