Relativistic hydrodynamic fluctuations from an effective action: causality, stability, and the information current

Causality is necessary for retarded Green's functions to remain retarded in all inertial frames in relativity, which ensures that dissipation of fluctuations is a Lorentz invariant concept. For first-order BDNK theories with stochastic fluctuations, introduced via the Schwinger-Keldysh formalism, we show that imposing causality and stability leads to correlation functions of hydrodynamic fluctuations that only display the expected physical properties at small frequencies and wavenumber, i.e., within the expected regime of validity of the first-order approach. For second-order theories of Israel and Stewart type, constructed using the information current such that entropy production is always non-negative, a stochastic formulation is presented using the Martin-Siggia-Rose approach where imposing causality and stability leads to correlators with the desired properties. We also show how Green's functions can be determined from such an action. We identify a $\mathbb{Z}_2$ symmetry, analogous to the Kubo-Martin-Schwinger symmetry, under which this Martin-Siggia-Rose action is invariant. This modified Kubo-Martin-Schwinger symmetry provides a new guide for the effective action formulation of hydrodynamic systems with dynamics not solely governed by conservation laws. Furthermore, this symmetry ensures that the principle of detailed balance is valid in a covariant manner. We employ the new symmetry to further clarify the connection between the Schwinger-Keldysh and Martin-Siggia-Rose approaches, establishing a precise link between these descriptions in second-order theories of relativistic hydrodynamics. Finally, the modified Kubo-Martin-Schwinger symmetry is used to determine the corresponding action describing diffusion in Israel-Stewart theories in a general hydrodynamic frame.Comment: 28 page

Far-from-equilibrium bulk-viscous transport coefficients in neutron star mergers

We investigate the weak-interaction-driven bulk-viscous transport properties of $npe$ matter in the neutrino transparent regime. Previous works assumed that the induced bulk viscosity correction to pressure, near beta equilibrium, is linear in deviations from the equilibrium charge fraction. We show that this is not always true for (some) realistic equations of state at densities between one and three times saturation density. This nonlinear nature of the perturbation around equilibrium motivates a far-from-beta-equilibrium description of bulk-viscous transport in neutron star mergers, which can be precisely achieved using a new Israel-Stewart formulation with resummed bulk and relaxation time transport coefficients. The computation of these transport coefficients depends on out-of-beta-equilibrium pressure corrections, which can be computed for a given equation of state. We calculate these coefficients for equations of state that satisfy the latest constraints from multi-messenger observations from LIGO/VIRGO and NICER. We show that varying the nuclear symmetry energy $J$ and its slope $L$ can significantly affect the transport coefficients and the nonlinear behavior of the out-of-equilibrium pressure corrections. Therefore, having better constraints on $J$ and $L$ will directly impact our understanding of bulk-viscous processes in neutron star mergers.Comment: 30 pages, 17 figures, 4 appendice

Hot QCD Phase Diagram From Holographic Einstein-Maxwell-Dilaton Models

In this review, we provide an up-to-date account of quantitative holographic descriptions of the strongly coupled quark-gluon plasma (QGP) produced in heavy-ion collisions, based on the class of gauge-gravity Einstein-Maxwell-Dilaton (EMD) models. Holography is employed to tentatively map the QCD phase diagram at finite temperature onto a dual theory of charged, asymptotically AdS black holes in 5D. With a quantitative focus on the hot QCD phase diagram, the EMD models reviewed are adjusted to describe lattice results for the finite-temperature QCD equation of state, with 2+1 flavors and physical quark masses, at zero chemical potential and vanishing electromagnetic fields. The predictive power of EMD models is tested by quantitatively comparing their predictions for the hot QCD equation of state at nonzero baryon density and the corresponding state-of-the-art lattice QCD results. The shear and bulk viscosities predicted by these EMD models are also compared to the corresponding profiles favored by the latest phenomenological multistage models describing different heavy-ion data. We report preliminary results from a Bayesian analysis which provide systematic evidence that lattice results at finite temperature and zero baryon density strongly constrains the free parameters of EMD models. Remarkably, the set of parameters constrained by lattice results at zero chemical potential produces EMD models in quantitative agreement with lattice QCD results also at finite baryon density. We also review results for equilibrium and transport properties from anisotropic EMD models, describing the QGP at finite temperatures and magnetic fields. Finally, we provide a critical assessment of the main limitations and drawbacks of the holographic models reviewed in the present work, and point out some perspectives we believe are of fundamental importance for future developments.Comment: Invited review, 73 pages, 14 figure

Transport coefficients of the quark-gluon plasma at the critical point and across the first-order line

A bottom-up Einstein-Maxwell-Dilaton holographic model is used to compute, for the first time, the behavior of several transport coefficients of the hot and baryon-rich strongly coupled quark-gluon plasma at the critical point and also across the first-order phase transition line in the phase diagram. The observables under study are of the shear and bulk viscosities, baryon diffusion, thermal conductivity, the jet quenching parameter $\hat{q}$, as well as the heavy-quark drag force and Langevin diffusion coefficients. These calculations provide a phenomenologically promising estimate for these coefficients, given that our model quantitatively reproduces lattice QCD thermodynamics results, both at zero and finite baryon density, besides naturally incorporating the nearly-perfect fluidity of the quark-gluon plasma. We find that the diffusion of baryon charge, and also the shear and bulk viscosities, are suppressed with increasing baryon density, indicating that the medium becomes even closer to perfect fluidity at large densities. On the other hand, the jet quenching parameter and the heavy-quark momentum diffusion are enhanced with increasing density. The observables display a discontinuity gap when crossing the first-order phase transition line, while developing an infinite slope at the critical point. The transition temperatures associated with different transport coefficients differ in the crossover region but are found to converge at the critical point.Comment: 18 pages, 13 figure

Equation of State and Energy Loss of Hot and Dense Quark-Gluon matter from Holographic Black Holes

By using gravity/gauge correspondence, we construct a holographic model, constrained to mimic the lattice QCD equation of state at zero density, to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the energy loss of light and heavy partons within the hot and dense plasma represented by the heavy quark drag force, Langevin diffusion coefficients and jet quenching parameter at the critical point and across the first-order transition line predicted by the model.Comment: 4 pages, proceedings for the 20th International Conference on Strangeness in Quark Matter (SQM2022

Bayesian location of the QCD critical point from a holographic perspective

A fundamental question in QCD is the existence of a phase transition at large doping of quarks over antiquarks. We present the first prediction of a QCD critical point (CP) from a Bayesian analysis constrained by first principle results at zero doping. We employ the gauge/gravity duality to map QCD onto a theory of dual black holes. Predictions for the CP location in different realizations of the model overlap at one sigma. Even if many prior samples do not include a CP, one is found in nearly 100% of posterior samples, indicating a strong preference for a CP.Comment: 5p, 4 figures + references + supplemental material (8p, 5 figures

Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data scienceComment: 70 pages, 3 figures, White Paper for the Long Range Plan for Nuclear Scienc