Non-Equilibrium Dynamics in QCD and Holography

TL;DR

The study addresses how to describe far-from-equilibrium QCD plasma in heavy-ion collisions and leverages holography to access strong-coupling dynamics. It analyzes three non-equilibrium/holographic scenarios in a strongly coupled $\mathcal{N}=4$ SYM plasma: anisotropic shear viscosity, anisotropic sound propagation in Bjorken expansion, and the non-equilibrium chiral magnetic effect, employing holographic duals such as the Vaidya metric and magnetic-field-enabled setups. Key findings include direction-dependent shear viscosities with distinct Kubo formulas, time-dependent $\eta(t_{avg})$ under isotropic non-equilibrium, anisotropic sound dispersion with two speeds $c_{||}$ and $c_\perp$, and CME signals highly sensitive to initial conditions and collision energy. Collectively, the results show that anisotropy and non-equilibrium markedly alter transport properties and support anisotropic hydrodynamics as a robust framework for QCD plasma, with implications for phenomenology and Bayesian calibration in heavy-ion analyses.

Abstract

The plasma generated in heavy ion collisions goes through different phases in its time evolution. While early times right after the collision are governed by far-from equilibrium dynamics, later times are believed to be well described by near-equilibrium dynamics. While the regimes of non-equilibrium are prohibitively complicated to describe within QCD, effective descriptions such as hydrodynamics provide a viable approach. In addition, holographic descriptions allow access to the full non-equilibrium dynamics at strong coupling. In this presentation, we review three examples of such hydrodynamic approaches and corresponding holographic descriptions: 1) non-equilibrium shear viscosity, 2) propagation of non-equilibrium sound waves, and 3) the non-equilibrium chiral magnetic effect.

Figures (5)

• Figure 1: Anisotropic specific shear viscosities in equilibrium. At increasing dimensionless magnetic field $\tilde{B} = B/T^2$ and nonzero chiral anomaly coefficient (parametrized by $\gamma=2/\sqrt{3}$), the longitudinal specific shear viscosity $\eta_{||}/s$ (colored diamonds) rapidly decreases towards large magnetic fields. Different colors correspond to the values of the dimensionless chemical potential $\mu/T$ indicated on the top. In contrast to that complex dependence, the transverse shear viscosity $\eta_\perp/s$ (dashed red line) is independent from magnetic field, temperature, chemical potential, and chiral anomaly coefficient.
• Figure 2: Isotropic non-equilibrium state and its holographic dual. Cold plasma is heated by an amount of energy during a time $\Delta t$.
• Figure 3: Isotropic non-equilibrium shear viscosity. The specific shear viscosity normalized to the value $1/(4\pi)$ is displayed, such that a holographic isotropic equilibrium plasma would have the value $\eta/s / (1/(4\pi))=1$.
• Figure 4: Thermodynamically defined speeds of sound in Bjorken expanding SYM plasma. Top: Speed of sound longitudinal to the Bjorken expansion (along the anisotropy). Bottom: Transverse speed of sound. Thick black lines indicate the $\mathcal{N}=4$ SYM sound attractor. Dashed lines indicate zeroth, first and second order hydrodynamic approximations, see Cartwright:2022hlg.
• Figure 5: Accumulated charge due to the time-integrated chiral magnetic effect current as function of collision energy. Different colors correspond to choice of different initial conditions for axial charge, energy density, and magnetic field (Case I-VI, see Cartwright:2021maz). Some cases lead to a larger charge accumulation at larger collision energy $s^{1/2}$, others lead to larger charge accumulation at smaller collision energies.