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 N_{f}≥2 massless flavors. We constrain conformal field theory (CFT) descriptions of a critical line in temperature T and imaginary baryon chemical potential θ_{B}=iμ_{B}/T. An 't Hooft anomaly at general θ_{B} constrains the transition even at θ_{B}=0, leaving only three minimal scenarios. The best-motivated scenario for N_{f}≥3, and perhaps also N_{f}=2, is beyond Ginzburg-Landau, featuring a conformal manifold of θ_{B}-dependent universality classes with an exactly marginal operator related to baryon density.