Loop equation and exact soft anomalous dimension in N = 4 super Yang-Mills

• Published in: The journal of high energy physics Vol. 2020; no. 6; p. 75
• Main Authors: Giombi, Simone, Komatsu, Shota
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020; Springer Nature B.V
• Subjects: Bosons; Classical and Quantum Gravitation; Contact angle; Contour milling; Elementary Particles; Gauge theory; High energy physics; Integrals; Localization; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetry; Two dimensional models; Yang-Mills theory; AdS-CFT Correspondence; Wilson; t Hooft and Polyakov loops; Supersymmetric Gauge Theory
• ISSN: 1029-8479
• DOI: 10.1007/JHEP06(2020)075

A bstract 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.