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

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.