Flavor-Dependence and Higher Orders of Gauge-Independent Solutions in Strong Coupling Gauge Theory

TL;DR

This paper reexamines the flavor dependence of non-perturbative solutions in strong coupling gauge theories, highlighting the importance of higher-order corrections for consistent critical coupling values and demonstrating slow convergence in the inversion method.

Contribution

It clarifies the flavor dependence of critical couplings in strong coupling gauge theories by connecting the inversion method with Schwinger-Dyson equations and analyzing higher-order effects.

Findings

Critical coupling in quenched QED reduces from 2π/3 to π/3 with higher-order corrections.

Higher-order corrections lead to slow convergence of the inversion method.

Flavor dependence affects the critical coupling values in strong coupling gauge theories.

Abstract

The fermion flavor $N_f$ dependence of non-perturbative solutions in the strong coupling phase of the gauge theory is reexamined based on the interrelation between the inversion method and the Schwinger-Dyson equation approach. Especially we point out that the apparent discrepancy on the value of the critical coupling in QED will be resolved by taking into account the higher order corrections which inevitably lead to the flavor-dependence. In the quenched QED, we conclude that the gauge-independent critical point $\alpha_c=2\pi/3$ obtained by the inversion method to the lowest order will be reduced to the result $\alpha_c=\pi/3$ of the Schwinger-Dyson equation in the infinite order limit, but its convergence is quite slow. This is shown by adding the chiral-invariant four-fermion interaction.