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

TL;DR

The paper identifies the dual (twisted) regime of Yang-Baxter deformed $ ext{O}(2N)$ sigma models with the twisted trigonometric $R$-matrix of type $D_N^{(2)}$, providing an explicit unitarizing factor $F_N( heta)$ and validating the picture via a detailed ATFT dual description. Using weak–strong duality between sigma models and affine Toda field theories, it derives a Toda description of the dual regime and, through a boson–fermion reinterpretation, a concrete Lagrangian form that enables perturbative scattering calculations. In the concrete $ ext{O}(4)$ case, the tree-level S-matrix matches the twisted $D_2^{(2)}$ $R$-matrix up to $F( heta)$, with the parametrization $x= ext{e}^{2oldsymbol{ mi} hetaoldsymbol{ ext{λ}}}$ and $k= ext{e}^{2ioldsymbol{ mi} hetaoldsymbol{ ext{λ}}}$ fixed by unitary and crossing constraints; these results motivate a general conjecture that the dual $ ext{O}(2N)$ theory is governed by $D_N^{(2)}$. The findings connect the dual regime to twisted quantum groups $U_q(rak{so}_{2N})$ and set up a path to extract TBA data and mass/UV properties via the twisted S-matrix, while highlighting open questions about a Lagrangian for the dual regime and possible extensions to other cosets.

Abstract

We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed $\mathrm{O}(2N)$ sigma models, which is a new one-parametric deformation of the $\mathrm{O}(2N)$ model. It can be obtained from the conventional YB deformed $\mathrm{O}(2N+2)$ sigma model by freezing two isometries. The scattering matrix in the non-deformed $\mathrm{O}(n)$ model is known to 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 $\mathrm{YB-O}(2N)$ 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 $\mathrm{YB-O}(2N)$. We find the corresponding unitarizing function $F_N(θ)$ explicitly, and, as a bonus, extract some physical properties of this system using the thermodynamic Bethe Ansatz technique.