2d Integrable field theories from 4d CS theory with 2d systems and its lattice discretization

The 4d Chern-Simons (CS) theory proposed by Costello,Yamazaki and Witten is proposed as a framework that allows a systematic description not only of (1+1)-d integrable lattice models, but also of 2d classical integrable field theories. This would allow for a unified description of the relationship between integrable lattice models and field theories in terms of a single gauge theory. In this talk, as a first step towards understanding this relation, I derive the Faddeev-Reshetikhin (FR) model, which can be discretised preserving the quantum integrability, from a 4d CS theory coupled with 2d free field theories. The derivation is based on my work [2012.07370] with K.Yoshida and O.Fukushima in Kyoto university. Then, I give a rough sketch of the lattice discretisation of the FR model in the context of 4d CS theory. This is achieved by discretising the 2d theory coupled to the 4d CS theory into Wilson lines, which would provide a framework for studying the lattice discretisation of 2d integrable field theories. The work on this discretisation is in progress with M.Yamazaki and M.Ashwinkumar in IPMU.

the 27th of September 2022, 14:30