Lattice Results for the Equation of State in Dense QCD-like Theories

We review the recent progress in Monte Carlo simulations of dense two-color QCD (QC2D), focusing on the phase diagram, the equation of state, and the sound velocity in the low-temperature regime. In three-color QCD at finite density, especially at low temperatures, the notorious sign problem makes lattice Monte Carlo simulations intractable. In contrast, QC2D is free from this issue due to the pseudoreality of the quark representation. Recent independent lattice studies have revealed unexpected phenomena through first-principles calculations of the phase structure and thermodynamics. A particularly notable finding is that the sound velocity exceeds the so-called conformal (holography) bound, cs2/c2≤1/3, which had not been observed in QCD-like theories at finite temperature. In this review, we focus primarily on results from a series of works by our group, along with related studies in dense QC2D and three-color QCD with isospin chemical potential. We discuss the possibility and physical implications of conformal bound violation even for three-color dense QCD, together with insights from effective model analyses and recent observations of neutron stars.