Order of the SU(Nf)×SU(Nf) chiral transition via the functional renormalization group

Abstract

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, formulated directly in d=3 spatial dimensions, with the inclusion of all possible (perturbatively) relevant and marginal operators, whose number is considerably larger than those in d=4. We find new, potentially infrared stable fixed points spanned throughout the entire Nf range. By conjecturing that the thermal chiral transition is governed by these “flavor continuous” fixed points, stability analyses 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 chiral transition for Nf=2, 3, 4, and makes it almost indistinguishable from a second-order one, if it 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. Published by the American Physical Society 2024