Lattice QCD at High Temperature and Density

TL;DR

This work surveys lattice QCD thermodynamics at finite temperature and density, detailing the lattice formulation, discretization schemes, and continuum extrapolation strategies used to study deconfinement and chiral symmetry restoration. It presents quantitative results for the QCD equation of state in the pure gauge theory and in QCD with light quarks, showing sizable deviations from the Stefan–Boltzmann limit up to a few times $T_c$ and highlighting nonperturbative screening effects. The analysis connects phase structure to observable quantities such as the Polyakov loop and chiral condensate, discusses the scaling behavior near the chiral limit, and gauges the impact of quark flavors on $T_c$, while addressing the sign problem and canonical approaches in finite-density QCD. Overall, the paper demonstrates progress toward a realistic, quantitatively predictive description of QCD thermodynamics and outlines the remaining challenges in simulating physical light-quark masses and finite density.

Abstract

After a brief introduction into basic aspects of the formulation of lattice regularized QCD at finite temperature and density we discuss our current understanding of the QCD phase diagram at finite temperature. We present results from lattice calculations that emphasize the deconfining as well as chiral symmetry restoring features of the QCD transition, and discuss the thermodynamics of the high temperature phase.

Figures (17)

• Figure 1: The QCD phase diagram of 3-flavour QCD with degenerate (u,d)-quark masses and a strange quark mass $m_s$.
• Figure 2: Deconfinement and chiral symmetry restoration in 2-flavour QCD: Shown is $\langle L\rangle$ (left), which is the order parameter for deconfinement in the pure gauge limit ($m_q\rightarrow \infty$), and $\langle \bar{\psi}\psi \rangle$ (right), which is the order parameter for chiral symmetry breaking in the chiral limit ($m_q\rightarrow 0$). Also shown are the corresponding susceptibilities as a function of the coupling $\beta=6/g^2$.
• Figure 3: Quark mass dependence of the Polyakov loop and chiral susceptibilities versus $m_{PS}/m_V$ for 3-flavour QCD. Shown are results from calculations with the improved gauge and staggered fermion action discussed in the Appendix.
• Figure 4: The left hand figure shows the heavy quark free energy in units of the square root of the string tension for the SU(3) gauge theory (open symbols) and three flavour QCD with light quarks (full symbols). The right hand figure gives the limiting value of the free energy normalized to the value at distance $r\simeq 0.23$ fm Kar01 as a function of temperature for the case of three flavour QCD. The quark mass used in the $n_f=3$ calculations corresponds to a ratio of pseudo-scalar and vector meson masses of $m_{PS} / m_V\simeq 0.7$.
• Figure 5: The pressure in QCD with different number of degrees of freedom as a function of temperature. The curve labeled (2+1)-flavour corresponds to a calculation with two light and a four times heavier strange quark mass Kar00a.