Comments on $η$-deformed principal chiral model from 4D Chern-Simons theory

Abstract: We study $\eta$-deformations of principal chiral model (PCM) from the viewpoint of a 4D Chern-Simons (CS) theory. The $\eta$-deformed PCM has originally been derived from the 4D CS theory by Delduc, Lacroix, Magro and Vicedo [arXiv:1909.13824]. The derivation is based on a twist function in the rational description. On the other hand, we start with a twist function in the trigonometric description and discuss possible boundary conditions. We show that a certain boundary condition reproduces the usual $\eta$-deformed PCM and another one leads to a new kind of Yang-Baxter deformation.