Order parameters and color-flavor center symmetry in QCD

Understand

Common lore suggests that $N$-color QCD with massive quarks has no useful order parameters which can be non-trivial at zero baryon density.

• However, such order parameters do exist when there are $n_f$ quark flavors with a common mass and $d\equiv\gcd(n_f,N) > 1$.
• These theories have a $\mathbb Z_d$ 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.