Massive current algebra in the many-flavor chiral Gross-Neveu model

TL;DR

This paper investigates the algebra of SU(n)-currents in the many-flavor chiral Gross-Neveu model, demonstrating the existence of non-local quantum charges and their implications for integrability.

Contribution

It provides a perturbative calculation of the current-current OPE in many-flavor models and proves its invariance under higher-order corrections, establishing non-local charges.

Findings

Non-local quantum charges exist in the models.

Higher-order corrections do not alter the OPE results.

Supports the integrability of the many-flavor chiral Gross-Neveu model.

Abstract

We study the algebra of SU(n)-currents in the many-flavor chiral Gross-Neveu model. The general structure of the current-current OPE leading to non-local quantum conserved charges is reviewed. We calculate the OPE in the one-flavor and the many-flavor models perturbatively and use renormalization group invariance to prove that our results are not altered by higher-order corrections. We conclude that in these models the non-local quantum charge exists which is the first step towards the proof of the absence of particle production and factorization.