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

Recent lattice evidence suggests the chiral phase transition in QCD is second-order for $N_f\ge 2$ massless flavors. We constrain CFT descriptions of a critical line in temperature $T$ and imaginary baryon chemical potential ${\theta }_B=i{\mu }_B\mathrm{/}T$. An 't Hooft anomaly at general ${\theta }_B$ constrains the transition even at ${\theta }_B=0$, leaving only three minimal scenarios. The best-motivated scenario for $N_f\ge 3$, and perhaps also $N_f=2$, is beyond Ginzburg-Landau, featuring a conformal manifold of ${\theta }_B$-dependent universality classes with an exactly marginal operator related to baryon density.