Quark–gluon thermodynamics with the ${Z}_{N_c}$ symmetry

Abstract

We investigate quark–gluon thermodynamics with the symmetry. The flavor-dependent twist boundary condition (TBC) is imposed on Nc degenerate flavor quarks in the SU(Nc) gauge theory. This model is useful to understand the mechanism of color confinement. Thermodynamics of this quark–gluon system is studied by imposing the TBC on the Polyakov-loop extended Nambu–Jona–Lasinio (PNJL) model. The TBC model is applied to two- and three-color cases. The symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. The color confinement below Tc preserves the flavor symmetry. Above Tc, the flavor symmetry is broken, but the breaking is suppressed by the entanglement between the Polyakov loop and the chiral condensate. Particularly at low temperature, dynamics of the TBC model is similar to that of the PNJL model with the standard fermion boundary condition, indicating that the symmetry is a good approximate concept in the latter model even if the current quark mass is small. The present prediction can be tested in future by lattice QCD, since the quark–gluon dynamics with a flavor-dependent imaginary chemical potential has no sign problem.

Instanton-dyon liquid model. V. Twisted light quarks

“…Since the localization of the zero-modes on a given instanton species is very sensitive to the nature of the the twist on S 1 , this deformation offers an insightful tool for the possible understanding of the fundamental aspects of the spontaneous breaking of chiral symmetry through the underlying topological constituents. Similar issues were addressed using PNJL models [19] and more recently monopole-dyons and without anti-monopole-dyons for small S 1 [21]. A numerical analysis in the the instanton-dyon liquid model with N f = N c = 2 was recently presented in [22].…”

“…General twisted fermionic boundary conditions on S 1 amounts to thermal QCD with Bohm-Aharanov phases that alter fundamentally the nature of the light quarks [17,18]. A particularly interesting proposal consists of a class of Z Nc twisted QCD boundary conditions with N c = N f resulting in a manifestly Z Nc symmetric QCD dubbed Z Nc -QCD [19]. The confined phase is both center and chiral symmetric eventhough the boundary conditions are flavor breaking.…”

“…The confined phase is both center and chiral symmetric eventhough the boundary conditions are flavor breaking. The deconfined phase is center and chiral symmetry broken [19,20].…”

QCD on a small circle

“…[44] (see also Refs. [45][46][47][48][49][50][51][52][53]). To preserve reflection (in the compactified direction) and charge conjugation symmetries, we also require that complex conjugation leave this set of eigenvalues unchanged.…”

“…However, in the special case of n f = N , the theory retains an intertwined Z N color-flavor center symmetry (see, e.g., Refs. [44,45]). 18 This symmetry combines the usual center transformation (2.3) with a cyclic permutation of quark flavors.…”