Order Parameters and Color-Flavor Center Symmetry in QCD.

Area of Science:

• Theoretical High Energy Physics
• Quantum Chromodynamics (QCD)
• Condensed Matter Physics

Background:

• Conventional understanding posits that N-color QCD with massive quarks lacks useful order parameters at zero baryon density.
• This limitation hinders the study of fundamental properties of quark matter under various conditions.

Purpose of the Study:

• To investigate the existence of useful order parameters in N-color QCD with massive quarks at zero baryon density.
• To explore the role of color-flavor center symmetry in theories with n_{f} quark flavors and d≡gcd(n_{f},N)>1.

Main Methods:

• Analysis of N-color quantum chromodynamics (QCD) with massive quarks.
• Investigation of Z_{d} color-flavor center symmetry arising from intertwined color center transformations and cyclic flavor permutations.
• Examination of symmetry realization dependence on temperature, baryon chemical potential, and the ratio n_{f}/N.

Main Results:

• Demonstration that useful order parameters exist in N-color QCD with massive quarks when n_{f} quark flavors share a common mass and d≡gcd(n_{f},N)>1.
• Identification of a Z_{d} color-flavor center symmetry in these theories.
• Found that the realization of this symmetry is contingent upon temperature, baryon chemical potential, and the n_{f}/N ratio.

Conclusions:

• The existence of non-trivial order parameters at zero baryon density in specific N-color QCD models challenges established lore.
• The identified Z_{d} color-flavor center symmetry provides a new framework for analyzing quark matter.
• These findings have significant implications for understanding the conformal window and dense quark matter.