On loop corrections to integrable 2D sigma model backgrounds

Abstract

We study regularization scheme dependence of β-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the β-function retains only two tensor structures up to certain terms containing ζ3. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and λ-deformed SU(2)/U(l) sigma models, for which these terms disappear.