Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories

TL;DR

This paper compares fundamental and adjoint fermions in SU(N) gauge theories, showing that with a twisted boundary condition, fundamental fermions can mimic adjoint fermions in symmetry and confinement properties, revealing new insights into gauge symmetry breaking.

Contribution

It introduces a flavor-dependent twisted boundary condition to fundamental fermions, enabling them to exhibit ZN symmetry and similar confinement dynamics as adjoint fermions in SU(N) gauge theories.

Findings

FTBC fundamental fermions exhibit ZN symmetry for any fermion mass.

PNJL model shows similar confinement/deconfinement dynamics between FTBC fundamental and adjoint fermions.

Potential gauge symmetry breaking observed for FTBC fundamental fermions.

Abstract

We investigate differences and similarities between fundamental fermions and adjoint fermions in SU(N) gauge theories. The gauge theory with fundamental fermions possesses ZN symmetry only in the limit of infinite fermion mass, whereas the gauge theory with adjoint fermions does have the symmetry for any fermion mass. The flavor-dependent twisted boundary condition (FTBC) is then imposed on fundamental fermions so that the theory with fundamental fermions can possess ZN symmetry for any fermion mass. We show similarities between FTBC fundamental fermions and adjoint fermions, using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. In the mean-field level, the PNJL model with FTBC fundamental fermions has dynamics similar to the PNJL model with adjoint fermions for the confinement/deconfinement transition related to ZN symmetry. The chiral property is somewhat different between the two models, but there is a simple relation between chiral condensates in the two models. As an interesting high-energy phenomenon, a possibility of the gauge symmetry breaking is studied for FTBC fundamental fermions.