Two-color quark matter: U(1)A restoration, superfluidity, and quarkyonic phase

We discuss the phase structure of quantum chromodynamics (QCD) with two colors and two flavors of light quarks. This is motivated by the increasing interest in the QCD phase diagram as follows: ( 1) The QCD critical point search has been under intensive dispute and its location and existence suffer from uncertainty of effective U(1)(A) symmetry restoration. ( 2) A new phase called quarkyonic matter is drawing theoretical and experimental attention but it is not clear whether it can coexist with diquark condensation. We point out that two-color QCD is nontrivial enough to contain essential ingredients for ( 1) and ( 2) both, and most importantly, is a system without the sign problem in numerical simulations on the lattice. We adopt the two-flavor Nambu-Jona-Lasinio model extended with the two-color Polyakov loop and make quantitative predictions that can be tested by lattice simulations.