Sums over representations of half-BPS Wilson loops in SYM matrix models are dual to bubbling wormhole geometries of multi-covered AdS5 x S5 with intersecting S4 boundaries.
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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Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
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Localization matrix models yield resummed strong-coupling expressions for observables in N=2 theories with antisymmetric and fundamental matter, using an effective 't Hooft coupling at large N.
Generic sum rules express arbitrary traces through convolutions of a single Laguerre polynomial for group character averages in Gaussian matrix models.
Holographic minimal-surface calculation maps the Gross-Ooguri phase transition for circular Wilson loops on the Coulomb branch and indicates tree-level exactness for the straight line.
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Holographic minimal-surface calculation maps the Gross-Ooguri phase transition for circular Wilson loops on the Coulomb branch and indicates tree-level exactness for the straight line.
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