Yang-Baxter sigma model from twistor space

We derive a novel two-field four-dimensional integrable field theory (IFT) from 6D holomorphic Chern-Simons theory on twistor space. The four-dimensional IFT depends on a skew-symmetric linear operator acting on a Lie algebra, and when this operator is specialized to a solution of the modified classical Yang-Baxter equation, the IFT develops a semilocal symmetry associated with this solution. The resulting 4D analog of the Yang-Baxter sigma model is related by symmetry reduction to the well-known 2D Yang-Baxter sigma model. An important implication that we find is the embedding of the equations of motion of the 2D Yang-Baxter sigma model in the anti-self-dual Yang-Mills equations. The 6D Chern-Simons theory on twistor space can alternatively be symmetry reduced to a 4D Chern-Simons theory configuration with disorder surface defects. The latter realizes the Yang-Baxter sigma model, implying a “diamond” for the Yang-Baxter sigma model obtained from twistor space. We also show that the homogeneous 2D Yang-Baxter sigma model can be derived from a limit of our setup.