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arXiv · 1802.01579

Gauge Theory and Integrability, II

Kevin Costello·Edward Witten·Masahito Yamazaki
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Abstract

Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine the corresponding quantum group deformations to all orders in $\hbar$ by deducing their RTT presentations. The arguments we give are a mix of familiar ones with reasoning that is more transparent from the four-dimensional gauge theory point of view. The arguments apply most directly for $\mathfrak{gl}_N$ and can be extended to all simple Lie algebras other than $\mathfrak{e}_8$ by taking into account the self-duality of some representations, the framing anomaly for Wilson operators, and the existence of quantum vertices at which several Wilson operators can end.

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Kevin Costello, Edward Witten, Masahito Yamazaki. 2018-02-05. Gauge Theory and Integrability, II. https://doi.org/10.4310/iccm.2018.v6.n1.a7

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