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$ε$-Expansion in the Gross-Neveu Model from Conformal Field Theory

Sudip Ghosh, Rajesh Kumar Gupta, Kasi Jaswin, Amin A. Nizami

TL;DR

The paper applies conformal-field-theory methods to the Gross-Neveu model near $d=2$ to compute leading-order anomalous dimensions of fermionic composites without Feynman diagrams. By matching two- and three-point functions at the UV fixed point and employing multiplet recombination, the authors derive recursion relations for the leading $\epsilon$-dependent anomalous dimensions and obtain explicit formulas for both basic fermion/fermion-scalar operators and higher composites. They also determine the anomalous dimension of a non-singlet scalar primary, finding new leading-order data. These results validate perturbative expectations for fermions and demonstrate a diagram-free approach that can be extended with bootstrap techniques to higher orders and more general operators.

Abstract

We compute the anomalous dimensions of a class of operators of the form $(\barψψ)^p$ and $(\barψψ)^pψ$ to leading order in $ε$ in the Gross-Neveu model in $2+ε$ dimensions. We use the techniques developed in arXiv: 1505.00963.

$ε$-Expansion in the Gross-Neveu Model from Conformal Field Theory

TL;DR

The paper applies conformal-field-theory methods to the Gross-Neveu model near to compute leading-order anomalous dimensions of fermionic composites without Feynman diagrams. By matching two- and three-point functions at the UV fixed point and employing multiplet recombination, the authors derive recursion relations for the leading -dependent anomalous dimensions and obtain explicit formulas for both basic fermion/fermion-scalar operators and higher composites. They also determine the anomalous dimension of a non-singlet scalar primary, finding new leading-order data. These results validate perturbative expectations for fermions and demonstrate a diagram-free approach that can be extended with bootstrap techniques to higher orders and more general operators.

Abstract

We compute the anomalous dimensions of a class of operators of the form and to leading order in in the Gross-Neveu model in dimensions. We use the techniques developed in arXiv: 1505.00963.

Paper Structure

This paper contains 11 sections, 107 equations, 10 figures.

Table of Contents

  1. Introduction
  2. The Gross-Neveu model
  3. Anomalous dimension of $\psi$, $\bar{\psi}$ and $\bar{\psi}\psi$
  4. Anomalous dimensions of $(\bar{\psi}\psi)^{p}$ and $(\bar{\psi}\psi)^{p}\psi$
  5. The structure of the OPEs
  6. Determining the coefficients in the OPE
  7. Recursion relations for the leading order anomalous dimensions
  8. Other scalar primaries
  9. Discussion
  10. Computation of $f_{2p}$ and $\rho_{2p}$
  11. Computation of $f_{2p+1}$ and $\rho_{2p+1}$

Figures (10)

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