Integrable deformations of the Breitenlohner–Maison model from 4d Chern–Simons theory

A bstract We derive integrable deformations of the 2d Breitenlohner–Maison (BM) sigma model that describes the stationary, axisymmetric sector of 4d general relativity, as well as higher-rank generalisations thereof, using the framework of 4d Chern–Simons theory. In particular, we consider deformations of the boundary conditions and action of the 4d Cole–Weck model, which lead to deformations of the BM model associated with solutions to the homogeneous and inhomogeneous classical Yang–Baxter equations respectively.