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

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.

12 pages, 16 figures

References in corpus (15)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The Phase Structure of the Polyakov--Quark-Meson Model
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop
• Thermodynamics of the PNJL model
• Critical endpoint in the Polyakov-loop extended NJL model
• Finite size phase transitions in QCD with adjoint fermions
• Polyakov loop extended NJL model with imaginary chemical potential
• New Phases of SU(3) and SU(4) at Finite Temperature
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Orbifold equivalence and the sign problem at finite baryon density
• The quarkynic phase and the Z_{Nc} symmetry
• Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited
• Deconfinement vs. chiral symmetry and higher representation matter

Cited by in corpus (28)

• Polyakov loop modeling for hot QCD
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Order parameters and color-flavor center symmetry in QCD
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• QCD on a small circle
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
• Anomaly matching in QCD thermal phase transition
• Understanding of QCD at high density from Z3-symmetric QCD-like theory
• From 3d dualities to hadron physics
• Critical behavior of gauge theories and Coulomb gases in three and four dimensions
• Vacuum structure of Yang-Mills theory as a function of $\theta$
• Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
• High-temperature domain walls of QCD with imaginary chemical potentials
• Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model
• Instanton-dyon Ensembles III: Exotic Quark Flavors
• Sign problem in $Z_3$-symmetric effective Polyakov-line model
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity
• Winding theta and destructive interference of instantons
• Recent progress in understanding deconfinement and chiral restoration phase transitions
• Finite-temperature phase transition of $N_f=3$ QCD with exact center symmetry
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses
• Phase structure and Hosotani mechanism in QCD-like theory with compact dimensions