Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions

TL;DR

This paper investigates the fermion mass spectrum in a two-dimensional scalar-fermion model with strong Wilson-Yukawa coupling, showing fermion doublers can be removed and only a neutral massive Dirac fermion remains.

Contribution

It demonstrates the removal of fermion doublers and characterizes the fermion spectrum in the strong coupling vortex phase of a 2D model, extending understanding of fermion-Higgs interactions.

Findings

Fermion doublers are eliminated in the VXS phase.

The lowest fermion spectrum is a neutral massive Dirac fermion.

Charged fermions are absent in the VXS phase.

Abstract

The fermion mass spectrum is studied in the quenched approximation in the strong coupling vortex phase (VXS) of a globally U(1)$_L \otimes$U(1)$_R$ symmetric scalar-fermion model in two dimensions. In this phase fermion doublers can be completely removed from the physical spectrum by means of a strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase consists most probably only of a massive Dirac fermion which has charge zero with respect to the $U(1)_L$ group. We give evidence that the fermion which is charged with respect to that subgroup is absent in the VXS phase. When the $U(1)_L$ gauge fields are turned on, the neutral fermion may couple chirally to the massive vector boson state in the confinement phase. The outcome is very similar to our findings in the strong coupling symmetric phase (PMS) of fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the exception that in four dimensions the neutral fermion does most probably decouple from the bosonic bound states.