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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 $θ$ into the dynamical mass generation of Pseudo quantum electrodynamics (PQED). The $θ$-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 $θ$ affects the critical parameters related to the fine-structure constant, $α_c(θ)$, and to the number of copies of the matter field, $N_c(θ)$, by favoring the symmetric phase. In the continuum limit ($Λ\to \infty$), nevertheless, the $θ$-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.