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

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.

arXiv comment21 pages and 1 figure, v2: references added, corrected error in regularization scheme change, typos fixed, appendix B extended, commented on connection to DVV metric, v3: typos fixed, published JHEP version

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• Grassmannian Sigma Models
• On First-Order GLSM for Sigma Models