Order of the SU(N_f) x SU(N_f) chiral transition via the functional renormalization group

Renormalization group flows of the SU(Nf)× SU(Nf) symmetric Ginzburg-Landau potential are calculated for a general number of flavors, Nf. Our approach does not rely on the ε expansion, but uses the functional renormalization group directly formulated in $d=3$ spatial dimensions with the inclusion of all possible (perturbatively) relevant and marginal operators. We find infrared fixed points spanned throughout the entire flavor number range that are inaccessible in the ε expansion. Stability analyses around the fixed points show that for Nf≥ 5 the chiral transition is of second-order, while for Nf=2,3,4, it is of first-order. We argue that the UA(1) anomaly controls the strength of the first-order transition, which could become almost continuous if the axial symmetry breaking is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the UA(1) symmetry breaking around the critical temperature.