Computation of Critical Exponent Eta at O(1/N_f^2) in Quantum Electrodynamics in Arbitrary Dimensions

TL;DR

This paper calculates the critical exponent eta at the second order in 1/N_f expansion for quantum electrodynamics in any number of dimensions, using Dyson equations and advanced Feynman diagram techniques.

Contribution

It provides a detailed method for evaluating the electron anomalous dimension at O(1/N_f^2) in arbitrary dimensions, including novel techniques for two-loop Feynman diagrams.

Findings

Computed eta at O(1/N_f^2) in arbitrary dimensions.

Developed methods for massless two-loop Feynman diagrams.

Enhanced understanding of critical behavior in QED.

Abstract

We present a detailed evaluation of $\eta$, the critical exponent corresponding to the electron anomalous dimension, at $O(1/N^2_{\!f})$ in a large flavour expansion of QED in arbitrary dimensions in the Landau gauge. The method involves solving the skeleton Dyson equations with dressed propagators in the critical region of the theory. Various techniques to compute massless two loop Feynman diagrams, which are of independent interest, are also given.