Phase Structure and Equation of State of Dense Strong-Interaction Matter

The understanding of matter at extreme temperatures or densities is of great importance since it is essential to various fundamental phenomena and processes, such as the evolution of the early universe or the description of astrophysical objects. Under such conditions, the governing interaction is the strong force between the elementary constituents of matter, i.e., quarks and gluons, which is described by quantum chromodynamics (QCD). In this work, we study the phase structure of dense strong-interaction matter with two massless quark flavors at finite temperature and the equation of state in the zero-temperature limit employing functional renormalization group techniques. Four-quark self-interactions, which play an essential role in the description of the strongly correlated low-energy dynamics, are fully incorporated in the sense of Fierz-complete interactions only constrained by symmetries. In order to analyze the importance of Fierz completeness and how incomplete approximations affect the predictive power, we study different versions of the Nambu–Jona-Lasinio model. The predictions from such low-energy effective models for dense QCD matter are of great interest as this regime is at least difficult to access with fully first-principles approaches such as lattice Monte Carlo techniques. We analyze the fixed-point and phase structure at finite temperature and quark chemical potential based on the RG flow of the four-quark interactions at leading order of the derivative expansion. By studying the relative strengths of the various four-quark couplings, we obtain insights into condensate formation in phases governed by spontaneous symmetry breaking. We find that Fierz completeness is particularly important at large quark chemical potentials and leads to a shift of the phase boundary to higher temperatures. The incorporation of dynamical gauge fields allows us to adopt an approach directly based on quark-gluon dynamics. Without any fine-tuning, we observe a natural emergence of dominances among the four-quark couplings indicating spontaneous chiral symmetry breaking at small chemical potentials and a color superconducting phase at high chemical potentials. These dominances are found to be very robust against details of the approximations in the gauge sector, indicating that the dynamics within the quark sector are crucial in this respect. Toward lower energy scales, we recast the RG flow in the form of a quark-meson-diquark-model truncation in order to access the regime governed by spontaneously broken symmetries. This allows us to derive for the first time constraints on the equation of state of cold isospin-symmetric QCD matter at high densities in a Fierz-complete setting directly anchored in the fundamental gauge theory. Our results are found to be remarkably consistent with chiral effective field theory approaches applicable at smaller densities and with perturbative QCD approaches at very high densities. At supranuclear densities, we observe that condensation effects are essential and give rise to a maximum in the speed of sound which exceeds the asymptotic non-interacting limit, with potential implications for astrophysical applications.