On β-function of N = 2 supersymmetric integrable sigma-models

Abstract

We study the regularization scheme dependence of Kähler (N = 2) supersymmetric sigma models. At the one-loop order the metric β function is the same as in the non-supersymmetric case and it coincides with the Ricci tensor. The first correction in the MS scheme is known to appear in the fourth loop [1, 2]. We show that for certain integrable Kähler backgrounds, such as the complete T-dual of η-deformed CPn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{CP}(n) $$\\end{document} sigma models, there is a scheme in which the fourth loop contribution vanishes.