On Integrable Deformations of CFTs and Integrable Two-Dimensional Sigma Models

In this paper, we analyze the systems of screening charges corresponding to $\eta$-deformed $O(N)$ and $OSp(N\mathrm{\mid }2m)$ sigma models. These sigma models can be represented as integrable deformations of certain conformal field theories. Based on the case of $O(N)$ sigma models, which were conjectured in previous works by A.V. Litvinov and co-authors to be an integrable deformation of the conformal field theory corresponding to the algebras $W(D(n+1\mathrm{\mid }n))$ and $W(D(n\mathrm{\mid }n))$ for the cases $N=2n+2$ and $N=2n+1$ at $n\ge 1$, respectively, we formulate a hypothesis on how to write down the system of screening charges for the conformal field theory whose integrable deformation defines the $\eta$-deformed $OSp(N\mathrm{\mid }2m)$ sigma model for the case of odd $N=2n+1$, asymptotically free models with $N-2m-2>0$ and $n\ge 2$, $m\ge 1$. This hypothesis is explicitly verified for the cases of $OSp(5\mathrm{\mid }2)$, $OSp(7\mathrm{\mid }2)$, and $OSp(7\mathrm{\mid }4)$, which were separately investigated in the work of M.N. Alfimov and co-authors.