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≡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.