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The nature and location of the QCD phase transition close to the chiral limitrestricts the phase structure of QCD with physical pion masses at non-vanishingdensity. At small pion masses, explicit $U(1)_{\rm A}$-breaking, as induced bya non-trivial topological density, is of eminent importance. It triggers the 'tHooft interactions and also manifests itself in the interplay of four-quarkinteractions at low momentum scales. In the present work, we perform aFierz-complete analysis of the emergence of four-quark interactions from theQCD dynamics at finite temperature, subject to a given 't Hooft coupling atlarge momentum scales. The variation of the latter allows us to test therobustness of our findings. Taking an estimate of the effect of the topologicalrunning of the 't Hooft coupling into account, our analysis suggests that thechiral transition in QCD with two massless quark flavours falls into the $O(4)$universality class.

Chiral and effective $U(1)_{\rm A}$ symmetry restoration in QCD