A heterotic integrable deformation of the principal chiral model

A novel classically integrable model is proposed. It is a deformation of the two-dimensional principal chiral model, embedded into a heterotic $\sigma$-model, by a particular heterotic gauge field. This is inspired by the bosonic part of the heterotic $\sigma$-model and its recent Hamiltonian formulation in terms of O$(d,d+n)$-generalised geometry by Hatsuda, Mori, Sasaki and Yata. Classical integrability is shown by construction of a Lax pair and a classical $\mathcal{R}$-matrix. Latter is almost of the canonical form with twist function and solves the classical Yang-Baxter equation.