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Quark Confinement from Correlation Functions

We study quark confinement by computing the Polyakov loop potential in Yang--Mills theory within different non-perturbative functional continuum approaches [1]. We extend previous studies in the formalism of the functional renormalisation group and complement those with findings from Dyson--Schwinger equations and two-particle-irreducible functionals. These methods are formulated in terms of low order Green functions. This allows to identify a criterion for confinement solely in terms of the low-momentum behaviour of correlators.