Does hot QCD have a conformal manifold in the chiral limit?

Motivated by recent lattice evidence for a second-order chiral phase transition in QCD in the chiral limit at generic $N_f$, I’ll discuss constraints on possible CFT descriptions of thermal criticality. A global 't Hooft anomaly, together with high-T and low-T input, leaves only three consistent scenarios for the transition, all requiring something exotic.  The best-motivated scenario is intrinsically beyond Ginzburg-Landau, and involves a conformal manifold of critical theories generated by an exactly marginal operator related to baryon density.