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

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.