Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets

Abstract

We consider $\sigma$-models on para-complex ${\mathbb{Z}}_T$-cosets, which are analogues of those on complex homogeneous target spaces considered recently by D. Bykov. For these models, we show the existence of a gauge-invariant Lax connection whose Poisson brackets are ultralocal. Furthermore, its light-cone components commute with one another in the sense of Poisson brackets. This extends a result of O. Brodbeck and M. Zagermann obtained twenty years ago for hermitian symmetric spaces.

arXiv comment19 pages

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• An elliptic integrable deformation of the Principal Chiral Model
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Integrable deformation of ${\mathbb{CP}}^n$ and generalised Kaehler geometry
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• Integrable models from 4d holomorphic BF theory