From field theory to superfluid hydrodynamics of dense quark matter

The study of quantum chromodynamics (QCD) at low temperatures and high densities is relevant for fundamental as well as applied astrophysical questions. On the fundamental side, the phase diagram of QCD at high and intermediate densities might be very complicated and its study is highly non-trivial. While heavy-ion collisions and lattice calculations are powerful tools to probe the phase structure in a regime of high temperatures and low densities, their applicability at higher densities is very limited. However, future accelerator facilities such as NICA might provide some insight (see for example Ref. [1]). Reliable information can be obtained in a region of asymptotically high densities, where QCD behaves like a free field theory and perturbative calculations are possible. The ground state in this region of the phase diagram is a color superconductor where quarks of all color and flavor form cooper pairs which was termed color-flavor locking (CFL) [2]. Among many interesting features of CFL that could be discussed at this point, two are particularly important for the following analysis: CFL spontaneously breaks chiral symmetry which leads to an octet of Goldstone bosons and furthermore, CFL spontaneously breaks baryon conservation U(1)B. Strictly speaking, perturbative calculations of for example the magnitude of the superconducting gap, are only valid at (rather exotic) values of the chemical potential of about μ ' 10 MeV and it is thus questionable whether CFL will persist all the way down to the phase boundary of nuclear matter. Going down in density, the increase in the mass of the strange quark will act as an external stress on the highly symmetric pairing pattern and systematic studies show [3], that CFL will most likely react by developing a kaon condensate. The corresponding ground state CFL-K is then subject to two symmetry breaking