Phases of strongly-interacting matter with functional methods

Non-perturbative aspects of strongly-interacting matter, in particular at non-vanishing temperatures, are investigated with functional methods. The consequences of confinement in terms of a linearly rising static quark potential arising from an infrared singular quark 4-point function are studied. Such a singularity is only consistent for a specific color structure and implies the existence of similar singularities in special color structures of n-point functions with n>3. A simple explanation for Casimir scaling is found within this mechanism of confinement.The deconfinement transition of fundamentally charged scalar and quark matter is investigated in terms of center symmetry. Novel dual order parameters are introduced that can be obtained from the corresponding matter propagators. In the case of quark matter the new order parameter compares well with the dual chiral condensate, with the advantage that no regularization is necessary even at non-vanishing quark masses.The influence of the axial anomaly on the chiral transition is studied in terms of a 't Hooft determinant with quarks and mesons as effective degrees of freedom in the functional renormalization group. In the case of two quark flavors, the calculated temperature dependent determinant results in a decrease of the anomalous eta'-mass close to the chiral transition temperature. This is connected to a partial Z(2) restoration at the chiral transition instead of the restoration of full axial U(1). With 2+1 quark flavors and a temperature independent 't Hooft term, the chiral transition is found to be of second order with three dimensional O(4) critical exponents in the limit of vanishing up and down quark mass, whereas a first-order transition is seen without U(1) violation. (author)