Algorithm for Computing the $\BETA$-Function of Quantum Electrodynamics in the Large N_f Expansion

TL;DR

This paper develops a method to compute the $eta$-function in quantum electrodynamics with many flavors using large $ ext{N}_f$ expansion, providing insights into critical exponents and higher order corrections.

Contribution

It introduces a novel approach to calculate the $eta$-function and critical exponents in QED at large $ ext{N}_f$, including a framework for higher order corrections.

Findings

Derived the critical exponent $eta'(g_c)$ in arbitrary dimensions.

Solved Dyson equations at $O(1/ ext{N}_f)$ in the large $ ext{N}_f$ expansion.

Presented a method for computing higher order corrections to $eta(g)$.

Abstract

By considering corrections to the asymptotic scaling functions of the photon and electron in quantum electrodynamics with $\Nf$ flavours, we solve the skeleton Dyson equations at $O(1/\Nf)$ in the large $\Nf$ expansion at the $d$-dimensional critical point of the theory and deduce the critical exponent $\beta^\prime(g_c)$, in arbitrary dimensions, and subsequently present a method for computing higher order corrections to $\beta(g)$.