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

TL;DR

This paper demonstrates the equivalence of beta functions in supersymmetric $CP^{n-1}$ sigma models and level-zero chiral Gross-Neveu models, confirming theoretical predictions through explicit four-loop calculations.

Contribution

It provides the first four-loop calculation of the beta function for the chiral Gross-Neveu model and discusses scheme dependence, supporting the conjectured all-loop beta function.

Findings

Beta functions of the two models coincide at four loops.

The four-loop calculation supports the all-loop conjecture.

Scheme dependence affects the renormalization process.

Abstract

We explain that the supersymmetric $CP^{n-1}$ 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 $CP^{n-1}$ 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.