Integrable Deformations of the Breitenlohner-Maison Model from 4d Chern-Simons Theory

TL;DR

This paper develops integrable deformations of the 2D Breitenlohner-Maison sigma model, derived from 4D Chern-Simons theory, connecting boundary condition modifications to solutions of classical Yang-Baxter equations.

Contribution

It introduces a novel framework linking 4D Chern-Simons theory to deformations of the BM model via boundary condition modifications and Yang-Baxter solutions.

Findings

Derived integrable deformations of the BM sigma model.

Connected boundary condition deformations to classical Yang-Baxter solutions.

Extended the framework to higher-rank generalisations.

Abstract

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.