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Loop equation and exact soft anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills

Author(s): Giombi, Simone; Komatsu, Shota

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Abstract: BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in N = 4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N , and make contact with the string worldsheet description at strong coupling. As an application of our results, we compute exactly a small-angle limit (and more generally near-BPS limits) of the cross anomalous dimension which governs the UV divergence of intersecting Wilson lines. The same quantity describes the soft anomalous dimension of scattering amplitudes of W -bosons in the Coulomb branch.
Publication Date: 10-Jun-2020
Electronic Publication Date: 10-Jun-2020
Citation: Giombi, Simone, Komatsu, Shota. (2020). Loop equation and exact soft anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills. Journal of High Energy Physics, 2020 (6), 10.1007/jhep06(2020)075
DOI: doi:10.1007/jhep06(2020)075
EISSN: 1029-8479
Keywords: AdS-CFT Correspondence, Supersymmetric Gauge Theory, Wilson, ’t Hooft and Polyakov loops
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Journal of High Energy Physics
Version: Final published version. This is an open access article.

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