Bounds on the Equation of State from QCD Inequalities
 and Lattice QCD

Determining the equation of state (EoS) of QCD matter at high baryon density from first principles is a vital challenge in modern nuclear theory because of its non-perturbative nature. The most promising method in the non-perturbative regime is lattice QCD, but it does not work at high baryon density due to the sign problem. However, there is a well-known exception to avoid the sign problem by taking opposite up and down quark chemicals; it is referred to as QCD at finite isospin chemical potential. In this talk, I describe the uses of QCD inequalities and input from the recent lattice QCD calculations at finite isospin chemical potential to derive robust bounds on the EoS at finite baryon density. We find that the lattice data puts an upper bound on the baryon density of the symmetric nuclear matter at a given baryon chemical potential and a lower bound on the pressure as a function of the energy density. I also discuss additional constraints from perturbative calculations of the QCD EoS at high density derived in earlier work and causality to delineate robust bounds on the EoS of isospin symmetric matter at densities relevant to heavy-ion collisions.

Reference:
Y. Fujimoto & S. Reddy, To appear in Phys. Rev. D [2310.09427]