Gauge Theory and Integrability, II

TL;DR

This paper explores the connection between four-dimensional gauge theories and solutions to the Yang-Baxter equation, deriving quantum group deformations to all orders in  using RTT presentations, with implications for various Lie algebras.

Contribution

It provides a novel derivation of quantum group deformations from gauge theory perspectives, extending to all simple Lie algebras except _8.

Findings

Derived quantum group deformations for rational, elliptic, and trigonometric solutions.

Extended the approach to all simple Lie algebras except _8.

Connected gauge theory methods with integrability and quantum groups.

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.