On loop corrections to integrable $2D$ sigma model backgrounds

TL;DR

This paper investigates how different regularization schemes affect the beta function in 2D sigma models, proposing a scheme that simplifies the beta function and applying it to specific deformed models to find explicit RG flow solutions.

Contribution

It introduces a regularization scheme that simplifies the beta function in 2D sigma models and provides explicit RG flow solutions for deformed models using this scheme.

Findings

The proposed scheme retains only two tensor structures in the beta function.

Explicit RG flow solutions are obtained for Yang-Baxter- and lambda-deformed models.

The scheme eliminates certain higher-order terms involving zeta_3 in the beta function.

Abstract

We study regularization scheme dependence of $\beta$-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the $\beta$-function retains only two tensor structures up to certain terms containing $\zeta_3$. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and $\lambda$-deformed $SU(2)/U(1)$ sigma models, for which these terms disappear.