QCD at a finite isospin density: Front the pion to quark-antiquark condensation

QCD at a finite isospin chemical potential mu (I) is studied. This theory h as no fermion-sign problem and can be simulated on a lattice by using prese nt-day techniques. We solve this theory analytically in two limits: low mu (I) where chiral perturbation theory is applicable, and asymptotically high mu (I), where perturbative QCD is at work. At a low isospin density, the g round state is a superfluid pion condensate. At a very high density, it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum number s as the pions. Motivated by this observation, we put forward a conjecture that the transition from hadron to quark matter is smooth. The conjecture p asses several nontrivial tests. Our results imply a nontrivial phase diagra m in the space of the temperature and chemical potentials of isospin and ba ryon number. At asymptotically large values of mu (I) and small values of t he baryon chemical potential, the ground state is in a phase similar to the Fulde-Ferrell-Larkin-Ovchinniltov phase, It is characterized by a spatiall y modulated superfluid order parameter <(u) over bar gamma (5)d > and may b e the asymptotic limit of the inhomogeneous pion-condensation phase advocat ed by Migdal and others. (C) 2001 MAIK "Nauka/Interperiodica".