Notices of the International Consortium of Chinese Mathematicians· 2018Q2
Gauge Theory And Integrability, I
- 121citations
- Q2SCImago
- 2018year
Short summary
Four-dimensional gauge theory systematically deduces solutions to the Yang-Baxter equation, including rational, trigonometric, and elliptic forms, via explicit Feynman diagram computations.
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Key points
- Four-dimensional gauge theory is shown to systematically generate solutions to the Yang-Baxter equation.
- Explicit computations via Feynman diagrams yield leading contributions to the R-matrix and operator product expansions.
- The framework explains the origin of rational, trigonometric, and elliptic solutions.
- A generalization, the dynamical Yang-Baxter equation, is also incorporated.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Notices of the International Consortium of Chinese Mathematicians, 2018 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics