Scattering in the dual regime of Yang-Baxter deformed O(2N) sigma models

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2026. Vol. 113. No. 6. Article 066007.

Bychkov A., Nekrasov B.

We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed $\OO(2N)$ sigma models, which is a new one-parametric deformation of the $\OO(2N)$ model. It can be obtained from the conventional YB deformed $\OO(2N+2)$ sigma model by freezing two isometries. The scattering matrix in the non-deformed $\OO(n)$ model is known coincide with the rational $\mathfrak{so}_n$-invariant $R-$matrix. For $n = 2N$ this rational solution allows for two trigonometric deformations: the usual $D_N^{(1)}$ and the twisted $D_{N}^{(2)}$. The usual one is known to coincide with the scattering matrix of the conventional YB-$\OO(2N)$ model. A natural question to ask is what sigma model corresponds to the twisted solution. In this work we claim that it is precisely our dual regime of YB-$\OO(2N)$. We find the corresponding unitarizing function $F_N(\theta)$ explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe Ansatz technique.

Keywords: анзац Бете, Bethe Ansatz, Уравнение Янга-Бакстера, Yang-Baxter equation, Integrable Field Theories, Sigma Models, интегрируемые модели квантовой теории поля, сигма-модели