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