Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class

TL;DR

This paper calculates critical exponents for fermion bilinear operators in the QED-Gross-Neveu universality class using large N techniques, confirming results with perturbative expansions and providing estimates in three dimensions.

Contribution

It provides the $O(1/N^2)$ critical exponents for fermion bilinear operators in the QED-Gross-Neveu class, extending previous results and validating them against perturbative calculations.

Findings

Critical exponents agree with three and four loop perturbative results.

Provides estimates of non-singlet operator exponents in three dimensions.

Confirms the validity of the large N formalism for this universality class.

Abstract

We use the critical point large $N$ formalism to calculate the critical exponents corresponding to the fermion mass operator and flavour non-singlet fermion bilinear operator in the universality class of Quantum Electrodynamics (QED) coupled to the Gross-Neveu model for an $SU(N)$ flavour symmetry in $d$-dimensions. The $\epsilon$ expansion of the exponents in $d$ $=$ $4$ $-$ $2\epsilon$ dimensions are in agreement with recent three and four loop perturbative evaluations of both renormalization group functions of these operators. Estimates of the value of the non-singlet operator exponent in three dimensions are provided.