Chiral symmetry breaking in dimensionally regularized nonperturbative quenched QED

TL;DR

This paper investigates dynamical chiral symmetry breaking in dimensionally regularized quenched QED using Dyson-Schwinger equations, providing both numerical and analytical insights into the critical coupling and solutions in various dimensions.

Contribution

It introduces a method to extract the critical coupling in quenched QED within dimensional regularization, extending previous cut-off based approaches and analyzing different vertex approximations.

Findings

Chiral symmetry breaking occurs for all couplings in D<4.

Analytic and numerical solutions for the Dyson-Schwinger equations are presented.

The critical coupling alpha_c = pi/3 is obtained from the D-dimensional theory.

Abstract

In this paper we study dynamical chiral symmetry breaking in dimensionally regularized quenched QED within the context of Dyson-Schwinger equations. In D < 4 dimensions the theory has solutions which exhibit chiral symmetry breaking for all values of the coupling. To begin with, we study this phenomenon both numerically and, with some approximations, analytically within the rainbow approximation in the Landau gauge. In particular, we discuss how to extract the critical coupling alpha_c = pi/3 relevant in four dimensions from the D dimensional theory. We further present analytic results for the chirally symmetric solution obtained with the Curtis-Pennington vertex as well as numerical results for solutions exhibiting chiral symmetry breaking. For these we demonstrate that, using dimensional regularization, the extraction of the critical coupling relevant for this vertex is feasible. Initial results for this critical coupling are in agreement with cut-off based work within the currently achievable numerical precision.