On dual regime in Yang-Baxter deformed $\mathrm{O}(2N)$ sigma models

TL;DR

The paper investigates a dual regime for Yang-Baxter deformed $O(2N)$ sigma models, arising from conformal perturbation theory and the associated screening systems. Unlike $O(2N+1)$, the $O(2N)$ case is not self-dual under $b^2 \leftrightarrow -1-b^2$, enabling a new perturbative description and a corresponding solution of the generalized Ricci flow. The authors derive explicit one-loop metrics $G_{\mu\nu}$ and $B_{\mu\nu}$ for the dual regime, and provide concrete realizations in the $O(4)$ and $O(6)$ cases, including connections to higher-sphere YB data and a general conjecture for all $2N$. These results bridge conformal perturbation theory, Toda/bowtie structures, and integrable sigma-model deformations, offering a new avenue to study the spectra and S-matrices of $O(2N)$ models via dual geometric data.

Abstract

In this paper, we explore a new class of integrable sigma models, which we refer to as the "dual regime" of Yang-Baxter (YB) deformed $\mathrm{O}(2N)$ sigma models. This dual regime manifests itself in the conformal perturbation approach. Namely, it is well known that conventional YB-deformed $\mathrm{O}(N)$ sigma models are described in the UV by a collection of free bosonic fields perturbed by some relevant operators. The holomorphic parts of these operators play the role of screening operators which define certain integrable systems in the free theory. All of these integrable systems depend on a continuous parameter $b$, which parametrizes the central charge, and are known to possess the duality under $b^2\longleftrightarrow -1-b^2$. Although $\mathrm{O}(2N+1)$ integrable systems are self-dual, $\mathrm{O}(2N)$ systems are not. In particular, the $\mathrm{O}(2N)$ integrable systems provide new perturbations of the sigma model type. We identify the corresponding one-loop metric and $B-$field and show that they solve the generalized Ricci flow equation.