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arXiv · 1709.09993

Gauge Theory and Integrability, I

Kevin Costello·Edward Witten·Masahito Yamazaki
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Abstract

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.

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Kevin Costello, Edward Witten, Masahito Yamazaki. 2017-09-28. Gauge Theory and Integrability, I. https://doi.org/10.4310/iccm.2018.v6.n1.a6

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