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Operator Product Expansions and Consistency Relations in a O(N) Invariant Fermionic CFT for 2<d<4

Anastasios C. Petkou

Abstract

A conformally invariant theory of Majorana fermions in 2<d<4 with O(N) symmetry is studied using Operator Product Expansions and consistency relations based on the cancellation of shadow singularities. The critical coupling G_{*} of the theory is calculated to leading order in 1/N. This value is then used to reproduce the O(1/N) correction for the anomalous dimension of the fermion field as evidence for the validity of our approach to conformal field theory in d>2.

Operator Product Expansions and Consistency Relations in a O(N) Invariant Fermionic CFT for 2<d<4

Abstract

A conformally invariant theory of Majorana fermions in 2<d<4 with O(N) symmetry is studied using Operator Product Expansions and consistency relations based on the cancellation of shadow singularities. The critical coupling G_{*} of the theory is calculated to leading order in 1/N. This value is then used to reproduce the O(1/N) correction for the anomalous dimension of the fermion field as evidence for the validity of our approach to conformal field theory in d>2.

Paper Structure

This paper contains 7 sections, 33 equations, 3 figures.

Table of Contents

  1. Introduction
  2. OPE's and Consistency Relations in a Fermionic $O(N)$ Invariant CFT in $2<d<4$
  3. The Free Theory
  4. The Non-Trivial Theory
  5. Summary and Outlook

Figures (3)

  • Figure 1: The graphical representation of $\langle\psi^{\alpha}_{i}(x_{1}){\bar{\psi}}^{\beta}(x_{2})\tilde{O}(x_{3})\rangle$.
  • Figure 2: Amputating the three-point function
  • Figure 3: The Skeleton Graph Expansion for $\Psi^{(\tilde{\eta}_{o})}_{ij,kl}(x_{1},x_{2};x_{3},x_{4})$