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

A bstract 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 CP(n) CP n sigma models, there is a scheme in which the fourth loop contribution vanishes.