Gauge Theory and Integrability, II

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 $\hslash$ 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.

51 pp

References in corpus (9)

• Supersymmetric gauge theory and the Yangian
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Non-local charges, Zm gradings and coset space actions
• Assembling integrable sigma-models as affine Gaudin models
• Integrable coupled sigma-models
• Integrable properties of sigma-models with non-symmetric target spaces
• Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
• Construction of Lax Connections by Exponentiation
• Integrability in Sigma-Models

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• Integrability of the $\lambda$-deformation of the PCM with spectators
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• Four-Dimensional Chern-Simons and Gauged Sigma Models
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
• Constraining all possible Korteweg-de Vries type hierarchies
• Quantizing local holomorphic field theories on twistor space
• Integrable Deformations of the Breitenlohner-Maison Model from 4d Chern-Simons Theory
• Integrable models from 4d holomorphic BF theory
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• Adjusting Higher Chern-Simons Theory