  The QCD axial anomaly, by coupling the chiral condensate and BCS pairing
fields of quarks in dense matter, leads to a new critical point in the QCD
phase diagram \cite{HTYB,chiral2}, which at sufficiently low temperature should
terminate the line of phase transitions between chirally broken hadronic matter
and color superconducting quark matter. The critical point indicates that
matter at low temperature should cross over smoothly from the hadronic to the
quark phase, as suggested earlier on the basis of symmetry. We review here the
arguments, based on a general Ginzburg-Landau effective Lagrangian, for the
existence of the new critical point, as well as discuss possible connections
between the QCD phase structure and the BEC-BCS crossover in ultracold trapped
atomic fermion systems at unitarity. and implications for the presence of quark
matter in neutron stars.
