Some exact results on the QCD critical point

We show, in a model-independent manner, that the QCD critical point can appear only inside the pion condensation phase of the phase-quenched QCD as long as the contribution of flavor-disconnected diagrams is negligible. The sign problem is known to be maximally severe in this region, implying that the QCD critical point is reachable by the present lattice QCD techniques only if there is an enhancement of the flavor-disconnected contribution at finite baryon chemical potential.