Order Parameters and Color-Flavor Center Symmetry in QCD

Common lore suggests that N-color QCD with massive quarks has no useful order parameters that can be nontrivial at zero baryon density. However, such order parameters do exist when there are n(f) quark flavors with a common mass and d equivalent to gcd(n(f), N) > 1. These theories have a Z(d) color-flavor center symmetry arising from intertwined color center transformations and cyclic flavor permutations. The symmetry realization depends on the temperature, baryon chemical potential, and value of n(f)/N, with implications for conformal window studies and dense quark matter.