QCD at finite density of isospin
Abstract :
QCD at finite isospin chemical potential mu_I has no fermion sign
problem and can be studied on the lattice. We solve this theory
analytically in two limits: at low mu_I where chiral perturbation
theory is applicable, and at asymptotically high mu_I where
perturbative QCD works. At low isospin density the ground state is a
pion condensate, whereas at high density it is a Fermi liquid with
Cooper pairing. The pairs carry the same quantum numbers as the pion.
This leads us to a conjecture that the transition from hadron to quark
matter is smooth, which passes several tests. Our results imply a
nontrivial phase diagram in the space of temperature and chemical
potentials of isospin and baryon number.
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