On the conformal limit of a QED-inspired model

TL;DR

This paper analyzes a conformal invariant QED-inspired model using Dyson-Schwinger equations, revealing new critical exponents and the interplay of multiple mass scales related to chiral symmetry breaking and wave function changes.

Contribution

It provides the first solution for the vector component exponent in a conformal QED-inspired model and generalizes previous scalar component results to linear covariant gauges.

Findings

Derived corrections to fermion propagator asymptotics as a function of coupling and gauge parameter.

Identified two critical exponents linked to chiral symmetry breaking and wave function changes.

Confirmed weak coupling results align with perturbative quenched QED analysis.

Abstract

A conformal invariant QED-inspired model is solved for a general covariant linear gauge using the Dyson-Schwinger equations for the propagators assuming a pure vector like interaction. The leading corrections to the asymptotic solutions and the exponents, that characterize the corrections to each of the two fermion propagator functions, are computed as a function of the coupling and gauge fixing parameter $\xi$. For the scalar component of the fermion propagator our findings generalizes for linear covariant gauges previous results found in the literature and reproduce the outcome of the perturbative analysis of quenched QED in the Landau gauge. Our solution for the exponent associated with vector component of the fermion propagator is new and, in the weak coupling regime, agrees with the estimation based on the perturbative analysis of quenched QED. Of the two critical exponents describing the conformal limit of the vector interaction, one of them is, in QED, associated with the regime where chiral symmetry is broken dynamically, which demands one mass scale, namely the Miransky scaling. A second mass scale has to be introduced at larger coupling constants and is associated with a change on the nature of the fermion wave function. This provides one example, that it is possible to find two interwoven cycles in Quantum Field Theory, albeit in a truncated framework, as it is known in the quantum few-body problem in the limit of a zero-range interaction.