Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane

TL;DR

This paper investigates how the Pseudo-Chern-Simons parameter influences dynamical mass generation in Pseudo quantum electrodynamics, revealing that it favors the symmetric phase and affects critical parameters at the classical level.

Contribution

It introduces the effects of the Pseudo-Chern-Simons parameter into PQED and analyzes its impact on critical parameters for mass generation using analytical and numerical methods.

Findings

The $ heta$-parameter influences the critical fine-structure constant $\alpha_c( heta)$.

The $ heta$-parameter affects the critical number of matter field copies $N_c( heta)$.

In the continuum limit, $ heta$ does not alter the critical parameters.

Abstract

Chiral symmetry breaking comes from the mass dynamically generated through interaction of Dirac fermions for both quantum electrodynamics in (2+1)D (QED3) and (3+1)D (QED4). In QED3, the presence of a Chern-Simons (CS) parameter affects the critical structure of the theory, favoring the symmetric phase where the electron remains massless. Here, we calculate the main effects of a Pseudo-Chern-Simons (PCS) parameter $\theta$ into the dynamical mass generation of Pseudo quantum electrodynamics (PQED). The $\theta$-parameter provides a mass scale for PQED at classical level and appears as the pole of the gauge-field propagator. After calculating the full electron propagator with the Schwinger-Dyson equation at quenched-rainbow and large-$N$ approximations, we conclude that $\theta$ affects the critical parameters related to the fine-structure constant, $\alpha_c(\theta)$, and to the number of copies of the matter field, $N_c(\theta)$, by favoring the symmetric phase. In the continuum limit ($\Lambda\to \infty$), nevertheless, the $\theta$-parameter do not affect the critical parameters. We also compare our analytical results with numerical findings of the integral equation for the mass function of the electron.