Dynamic critical behavior of hot and dense QCD matter from the real-time functional renormalization group

Abstract

In this work, we study dynamic critical behavior of hot and dense QCD matter near second-order phase transitions. We consider the chiral phase transition for two flavors of massless quarks, as well as the conjectured critical point at physical quark masses and finite baryon chemical potential. These are plausibly in the same dynamic universality classes as a four-component Heisenberg antiferromagnet and the liquid-gas critical point of a pure fluid, respectively, whose critical dynamics are described by Models G and H in the Halperin-Hohenberg classification. Our central tool in this work is a real-time generalization of the functional renormalization group (FRG) based on the Schwinger-Keldysh contour. Starting with Model G, we develop a novel formulation of the real-time FRG which preserves all relevant symmetries of dynamical systems with reversible mode couplings. We show that associated Ward identities imply exact statements about the FRG flow, including the non-renormalization of the mode-coupling constant, and the independence of the static free energy on the dynamics. We show that the formalism reproduces the non-trivial value z=d/2 for the dynamic critical exponent in d spatial dimensions, and we compute a novel scaling function which describes the universal temperature and momentum dependence of the iso-vector and iso-axial-vector charge diffusion coefficient in the chiral limit. As a next step, we adapt this novel FRG technique to Model H. We derive analytical expressions for dynamic critical exponents that describe the universal power-law divergence of the heat conductivity and the shear viscosity near the QCD critical point. As a central result, we find that the critical exponent of the shear viscosity as a function of d exhibits a maximum in the range 2 < d < 4 and approaches zero for d=2 spatial dimensions. We verify the robustness of this result by considering improved truncations of the static free energy. In parallel, we emphasize the structural similarities and differences with Model G by comparing the fixed-point structures of both models and discuss the presence/absence of weak and strong dynamic scaling relations. While the leading universal scaling behavior can be described by Models G and H, non-universal corrections require a real-time description of the microscopic dynamics. In this regard, we consider a real-time formulation of the quark-meson model as a particular low-energy effective theory for QCD. As a first application, we study the influence of bosonic dissipation on the phase diagram and the excitation spectrum. We find that dissipation has a non-vanishing but quantitatively small effect on equilibrium observables. The influence on the excitation spectrum, on the other hand, can be drastic, as (over-)damping potentially turns weakly-damped quasiparticles into purely relaxational excitations.