On Calculation of 1/n Expansions of Critical Exponents in the Gross-Neveu Model with the Conformal Technique

TL;DR

This paper proves critical conformal invariance for a broad class of models and introduces a method to determine critical exponents using conformal bootstrap, exemplified on the Gross-Neveu model.

Contribution

It presents a new method for establishing critical conformal invariance and calculates critical exponents in the Gross-Neveu model up to high orders.

Findings

Critical conformal invariance proven for wide class of models.

Calculated critical exponents ilde{ au} at order 1/n^3, eta at order 1/n^2, and 1/ u at order 1/n^2.

Method demonstrated with explicit example of the Gross-Neveu model.

Abstract

A proof of critical conformal invariance of Green's functions for a quite wide class of models possessing critical scale invariance is given. A simple method for establishing critical conformal invariance of a composite operator, which has a certain critical dimension, is also presented. The method is illustrated with the example of the Gross--Neveu model and the exponents \et\ at order $1/n^3$, \Dl\ and $1/\nu$ at order $1/n^2$ are calculated with the conformal bootstrap method.