Building models of quarks and gluons with an arbitrary number of colors using Cartan-Polyakov loops

Abstract

In this work we introduce the concept of Cartan-Polyakov loops, a special subset of Polyakov loops in the fundamental representation of the $\mathrm{SU}(N_c)$ group, with charges $k=1,\dots ,(N_c-1)/2$. It constitutes a sufficient set of independent degrees of freedom and it is used to parametrize the thermal Wilson line. Polyakov loops not contained in this set are classified as non-Cartan-Polyakov loops. Using properties of the characteristic polynomial of the thermal Wilson line, we write a non-Cartan-Polyakov loop charge decomposition formula. This formalism allows one to readily build effective models of quarks and gluons with an arbitrary number of colors. We apply it to the Polyakov$-$Nambu$-$Jona-Lasinio model and to an effective glue model, in the mean field approximation, showing how to directly extend these models to higher values of $N_c$.

28 pages

References in corpus (18)

• The Phase Structure of the Polyakov--Quark-Meson Model
• Mesonic correlation functions at finite temperature and density in the Nambu-Jona-Lasinio model with a Polyakov loop
• Renormalized Polyakov loops in many representations
• Improved Polyakov-loop potential for effective models from functional calculations
• Tetraquarks in large-$N_c$ QCD
• The nuclear liquid-gas phase transition at large $N_c$ in the Van der Waals approximation
• Polyakov loop fluctuations and deconfinement in the limit of heavy quarks
• Large-$N_c$ analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms
• The Large $N_c$ limit of QCD on the lattice
• Hybrid stars with large strange quark cores constrained by GW170817
• The fate of the critical endpoint at large $N_c$
• Fluctuations of order parameter in an $SU(N_c)$ effective model
• QCD Phase Diagram by Holography
• The strange critical endpoint and isentropic trajectories in an Extended PNJL Model with Eight Quark Interactions
• Baryon axial vector current in large-$N_c$ chiral perturbation theory: Complete analysis for $N_c=3$
• Consistent approach to study gluon quasi-particles
• Parton physics of the large-$N_c$ mesons
• Diagrammatic Young Projection Operators for U(n)