2017/09/28 by Kevin Costello, Edward Witten, Masahito Yamazaki · 1 voice
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #hep-th #math.QA
paper · pdf · doi:10.4310/iccm.2018.v6.n1.a6
published as ICCM Not. 6, 46-119 (2018) · 141 pp
arxiv published 2017/09/28 · arxiv created 2018/02/04 · arxiv updated 2019/04/23
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 \mathfrakg[[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.