Gauge Theory And Integrability, II

• DOI: 10.4310/iccm.2018.v6.n1.a7
• Publication Date: 2018-09-14T16:36:03Z
• Authors: Kevin Costello; Edward Witten; Masahito Yamazaki
• Keywords: High Energy Physics - Theory; High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Mathematics - Quantum Algebra; 0103 physical sciences; FOS: Mathematics; Quantum Algebra (math.QA); FOS: Physical sciences; 01 natural sciences; Condensed Matter - Statistical Mechanics

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in many details, and present the arguments in a concrete and down-to-earth way. Many interesting effects, including the leading nontrivial contributions to the $R$-matrix, the operator product expansion of line operators, the framing anomaly, and the quantum deformation that leads from $\mathfrak{g}[[z]]$ to the Yangian, are computed explicitly via Feynman diagrams. We explain how rational, trigonometric, and elliptic solutions of the Yang-Baxter equation arise in this framework, along with a generalization that is known as the dynamical Yang-Baxter equation.<br/>141 pp<br/>