Equation of state of QCD(-like) theory using Lattice Monte Carlo simulations

Abstract

The equation of state (EoS) of strongly interacting matter at low temperature and high baryon density is a central ingredient in the physics of compact stars, but it is still difficult to determine directly from first-principles QCD calculations because of the sign problem. Two-colour QCD (QC$_2$D) provides a useful and controllable laboratory: for an even number of fundamental flavours the fermion determinant is real and positive, while the theory shares the nonperturbative properties with three-colour QCD at least zero chemical-potential regime. In this short review we summarize recent lattice progress on dense QC$_2$D, with emphasis on the phase structure, the emergence of superfluidity, the Bose--Einstein-condensation (BEC) to Bardeen--Cooper--Schrieffer(BCS) crossover, and thermodynamic quantities. A particularly interesting outcome is that the sound velocity in the cold dense superfluid regime can exceed the conformal value $c_{\rm s}^2/c^2=1/3$. This behaviour, now seen in the simulations for several QCD-like theories, gives a stiff strongly interacting matter. It is expected to offer insight into at least some aspects of the physics realized inside neutron stars.