Center-symmetric Landau gauge: Further signatures of confinement

In a recent article [D. M. van Egmond and U. Reinosa, Phys. Rev. D 106, 074005 (2022)PRVDAQ2470-001010.1103/PhysRevD.106.074005], we have identified new signatures for the Yang-Mills deconfinement transition, based on the finite-temperature longitudinal or (chromo-)electric gluon propagator as computed in the center-symmetric Landau gauge. Here, we generalize these considerations into a systematic study of the center symmetry identities obeyed by the correlation functions in this gauge. Any violation of these constraints signals the breaking of center symmetry and can thus serve as a probe for the deconfinement transition.