Quantum distillation in QCD

We propose a grading protocol that assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the image of quantum distillation in terms of (nondynamical) flavor holonomy dependence of (dynamical) gauge-holonomy potentials, in QCD with N-f = N-c fundamental and one massive adjoint fermion on R-3 x S-1. The compactified theory possesses an exact zero-form color-flavor center symmetry for a special choice of flavor holonomy (under which Polyakov loop is charged), despite the absence of one-form center symmetry. We prove that the color-flavor center symmetry is stable at small beta. This is the opposite of the high-temperature limit of thermal theory and a dramatic manifestation of quantum distillation. We show chiral symmetry breaking at small S-1 and that the vacuum structure of the theory on R-4 and R-3 x S-1 are controlled by the same mixed 't Hooft anomaly condition.