Does Hot QCD Have a Conformal Manifold in the Chiral Limit

Recent lattice evidence may suggest the chiral phase transition in QCD is second order for Nf≥2 massless flavors. We constrain conformal field theory (CFT) descriptions of a critical line in temperature T and imaginary baryon chemical potential θB=iμB/T. An 't Hooft anomaly at general θB constrains the transition even at θB=0, leaving only three minimal scenarios. The best-motivated scenario for Nf≥3, and perhaps also Nf=2, is beyond Ginzburg-Landau, featuring a conformal manifold of θB-dependent universality classes with an exactly marginal operator related to baryon density.