Confinement from correlation functions

We compute the Polyakov loop potential in Yang-Mills theory from the fully dressed primitively divergent correlation functions only. This is done in a variety of functional approaches ranging from functional renormalization group equations over Dyson-Schwinger equations to two-particle irreducible functionals. We present a confinement criterion that links the infrared behavior of propagators and vertices to the Polyakov loop expectation value. The present work extends the works of J. Braun et al., Phys. Lett. B 684, 262 (2010); F. Marhauser and J. M. Pawlowski, arXiv:0812.1144; J. Braun et al., Eur. Phys. J. C 70, 689 (2010) to general functional methods and sharpens the confinement criterion presented there. The computations are based on the thermal correlation functions in the Landau gauge calculated in L. Fister and J. M. Pawlowski, arXiv:1112.5440; L. Fister and J. M. Pawlowski, arXiv:1112.5429; L. Fister, Ph.D. thesis, Heidelberg University, 2012.