[Paper Review] Dense and Hot QCD at Strong Coupling

Tuna Demircik, Christian Ecker+1 more|arXiv (Cornell University)|Dec 22, 2021

Pulsars and Gravitational Waves Research98 references4 citations

TL;DR

This paper presents a thermodynamically consistent equation of state for dense and hot QCD by combining holographic V-QCD at high densities, a van der Waals model with excluded volume corrections for nuclear matter, and the DD2 statistical model for nuclear matter. It predicts a critical end point in the QCD phase diagram near T ≈ 110–120 MeV and n_b ≈ 0.3–0.4 n_s, with three EoS variants (soft, intermediate, stiff) all compatible with neutron star observations and lattice QCD constraints.

ABSTRACT

We present a novel framework for the equation of state of dense and hot Quantum Chromodynamics (QCD), which focuses on the region of the phase diagram relevant for neutron star mergers and core-collapse supernovae. The model combines predictions from the gauge/gravity duality with input from lattice field theory, QCD perturbation theory, chiral effective theory and statistical modeling. It is therefore, by construction, in good agreement with theoretical constraints both at low and high densities and temperatures. The main ingredients of our setup are the non-perturbative V-QCD model based on the gauge/gravity duality, a van der Waals model for nucleon liquid, and the DD2 version of the Hempel-Schaffner-Bielich statistical model of nuclear matter. By consistently combining these models, we also obtain a description for the nuclear to quark matter phase transition and its critical endpoint. The parameter dependence of the model is represented by three (soft, intermediate and stiff) variants of the equation of state, all of which agree with observational constraints from neutron stars and their mergers. We discuss resulting constraints for the equation of state, predictions for neutron stars and the location of the critical point.

Motivation & Objective

• To construct a thermodynamically consistent equation of state (EoS) for dense and hot QCD across the phase diagram, especially relevant for neutron star mergers and core-collapse supernovae.
• To bridge the gap in theoretical modeling at intermediate densities (n ≈ 0.16–1.0 fm⁻³) and temperatures up to 100 MeV, where first-principles methods like lattice QCD and perturbation theory fail.
• To accurately describe the nuclear-to-quark matter phase transition and estimate the location of the critical end point using a hybrid model framework.
• To ensure consistency with observational constraints from neutron stars (e.g., GW170817 tidal deformability) and lattice QCD data at low densities.

Proposed method

• Uses the holographic V-QCD model based on gauge/gravity duality to describe quark matter and the nuclear-to-quark matter phase transition at high densities.
• Applies an excluded volume corrected van der Waals model for nuclear matter to incorporate temperature dependence, calibrated to match V-QCD at zero temperature.
• Combines the V-QCD and van der Waals models with the DD2 version of the Hempel-Schaffner-Bielich statistical model to ensure consistency across the full density and temperature range.
• Employs a meson gas model near the QCD crossover region to improve finite-temperature behavior in the hadronic phase.
• Uses a 5th-order polynomial fit to the latent heat across the first-order transition region to extrapolate to the critical point where latent heat vanishes.
• Determines the critical end point by computing the geometric mean of baryon number densities on the transition lines at the critical temperature.

Experimental results

Research questions

• RQ1 Where is the critical end point located in the QCD phase diagram for dense and hot matter, and how does its position depend on the equation of state?
• RQ2 How can a thermodynamically consistent equation of state be constructed across the entire range of densities and temperatures relevant to neutron star mergers and core-collapse supernovae?
• RQ3 What is the role of excluded volume corrections in modeling the temperature dependence of the nuclear matter equation of state, and how do they affect the phase transition structure?
• RQ4 How well do the resulting EoS variants (soft, intermediate, stiff) agree with observational constraints from neutron stars and lattice QCD data?
• RQ5 Can a unified description of nuclear and quark matter phases be achieved using holographic models and effective nuclear theories in a consistent thermodynamic framework?

Key findings

• The critical temperature for the nuclear-to-quark matter phase transition is estimated to be T_c ≈ 115–120 MeV, with the critical end point located at n_bc ≈ 0.35n_s for the soft EoS and n_bc ≈ 0.4n_s for the intermediate and stiff variants.
• The latent heat of the first-order phase transition decreases with increasing temperature and vanishes at T_c, indicating a crossover transition at high temperatures.
• The best-fit excluded volume parameter is v₀ ≈ 0.56 fm⁻³, which yields a physically natural potential with long-range attraction and short-range repulsion, avoiding unphysical intermediate repulsion.
• The three EoS variants (soft, intermediate, stiff) all satisfy observational constraints from neutron star masses and tidal deformability measurements, including GW170817.
• The model shows good agreement with lattice QCD data at low densities and with ab initio calculations at low temperatures, validating its consistency across theoretical regimes.
• The critical point location is estimated with uncertainty below 0.05n_s for the soft EoS and below 0.1n_s for the others, indicating robustness despite model uncertainties.