Gauge Theory and Boundary Integrability II: Elliptic and Trigonometric Case

Abstract

We consider the mixed topological-holomorphic Chern-Simons theory introduced by Costello, Yamazaki and Witten on a ${\mathbb{Z}}_2$ orbifold. We use this to construct semi-classical solutions of the boundary Yang-Baxter equation in the elliptic and trigonometric cases. A novel feature of the trigonometric case is that the ${\mathbb{Z}}_2$ action lifts to the gauge bundle in a $z$-dependent way. We construct several examples of $K$-matrices, and check they agree with cases appearing in the literature.

arXiv comment32 pages, 6 figures

References in corpus (8)

• Quantum symmetric Kac-Moody pairs
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Four-Dimensional Avatars of Two-Dimensional RCFT
• Gauge Theory and Integrability, II
• Gauge Theory and Integrability, I
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• $A_{n-1}^{(1)}$ Reflection K-Matrices
• Gauge Theory and Boundary Integrability

Cited by in corpus (4)

• 4-dimensional Chern-Simons theory and integrable field theories
• Superspin Chains Solutions from 4D Chern-Simons Theory
• The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach
• Integrable Lattice Models and Holography