Integrable Lattice Models and Holography

Abstract

We study four-dimensional Chern-Simons theory on $D\times \mathbb{C}$ (where $D$ is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an "analytically-continued" toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary correlation functions of local operators in the three-dimensional WZW model. In particular, we reproduce the leading and subleading nontrivial contributions to the rational R-matrix purely from the boundary theory.

arXiv comment22 pages, 8 figures. Additional discussions and minor improvements. Published in JHEP

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Cited by in corpus (5)

• 4-dimensional Chern-Simons theory and integrable field theories
• Higher Gauge Theory and Integrability
• 4d Chern-Simons Theory as a 3d Toda Theory, and a 3d-2d Correspondence
• Topological 4D gravity and gravitational defects
• 5d-4d Correspondence in Twisted M-theory on a Conifold