$\beta$-function of the level-zero Gross-Neveu model

Abstract

We explain that the supersymmetric {CP}^{n-1}CPn−1 sigma model is directly related to the level-zero chiral Gross-Neveu (cGN) model. In particular, beta functions of the two theories should coincide. This is consistent with the one-loop-exactness of the {CP}^{n-1}CPn−1 beta function and a conjectured all-loop beta function of cGN models. We perform an explicit four-loop calculation on the cGN side and discuss the renormalization scheme dependence that arises.