Analysis of Abelian Gauge Theory with Four Fermi Interaction at $O(1/N^2)$ in Arbitrary Dimensions

TL;DR

This paper derives a general expression for the anomalous dimension of the fermion field in an Abelian gauge theory with four-Fermi interaction at the second order in 1/N expansion across arbitrary dimensions, enhancing understanding of quantum field behavior.

Contribution

It provides a novel, dimension-independent formula for the fermion anomalous dimension at O(1/N^2) in Abelian gauge theories with four-Fermi interactions.

Findings

Derived a general expression for the anomalous dimension in arbitrary dimensions.

Extended large N expansion results to second order in 1/N.

Applicable to models with U(1) gauge fields and four-Fermi interactions.

Abstract

An arbitrary dimensional expression is given for the anomalous dimension of the fermion field in a model with a four point interaction and a $U(1)$ gauge field, at $O(1/N^2)$ within a large flavour expansion in the Landau gauge.