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

Giombi, Simone; Komatsu, Shota

doi:10.1007/jhep06(2020)075

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

Journal Article · Wed Jun 10 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep06(2020)075· OSTI ID:1737766

Giombi, Simone ^[1]; Komatsu, Shota ^[2]

Princeton Univ., NJ (United States)
Inst. for Advanced Study, Princeton, NJ (United States)

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 $$ \mathcal{N} $$ = 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.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: SC0009988; PHY-1620542; PHY-1914860

OSTI ID:: 1737766

Journal Information:: Journal of High Energy Physics (Online), Vol. 2020, Issue 6; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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