Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation

TL;DR

This paper develops a gauge-invariant fermion-boson vertex ansatz that improves the understanding of chiral symmetry breaking and confinement in QED, applicable in both 3D and 4D, and reduces gauge dependence in critical phenomena.

Contribution

The authors propose a simple, practical vertex ansatz that ensures gauge covariance, reproduces perturbation theory, and achieves gauge-independent results for DCSB and confinement in QED models.

Findings

Reduces gauge dependence of critical coupling in qQED4.

Provides gauge-independent order parameters for confinement and DCSB in qQED3.

Improves upon the Curtis-Pennington vertex construction.

Abstract

A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart (qQED3). Employing this convenient form of the vertex \emph{ansatz} into the Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it renders the critical coupling in qQED4 markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and DCSB in qQED3.