Center phase transition from matter propagators in (scalar) QCD

Novel order parameters for the confinement-deconfinement phase transition of quenched QCD and fundamentally charged scalar QCD are presented. Similar to the well-known dual condensate, they are defined via generalized matter propagators with $U(1)$-valued boundary conditions. The order parameters are easily accessible with functional methods. Their validity and accessibility is explicitly demonstrated by numerical studies of the Dyson-Schwinger equations for the matter propagators. Even in the case of heavy scalar matter, where the propagator does not show a signature of the phase transition, a discontinuity due to the transition can be extracted in the order parameters, establishing also fundamentally charged scalar matter as a probe for color confinement.