Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics (0804.1950v1)

Abstract: We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first order transition, we observe a sharp rise in zeta/s near T_c. For constructions that exhibit a smooth cross-over, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.

• The paper introduces novel black hole models as duals to QCD by breaking conformal symmetry to mimic finite temperature thermodynamics and phase transitions.
• It employs the AdS/CFT framework with tailored scalar potentials to compute key properties like the bulk viscosity to entropy density ratio, noting a sharp rise near T₍c₎.
• The findings imply that tuning gravitational dual parameters can effectively replicate QCD plasma behavior, providing actionable insights for lattice and experimental studies.

An Examination of Thermodynamic Equilibria and Bulk Viscosity in Black Hole Analogs of Finite Temperature QCD

The paper, authored by Steven S. Gubser, Abhinav Nellore, Silviu S. Pufu, and Fabio D. Rocha, focuses on the thermodynamics and bulk viscosity of particular black hole solutions that bear approximate duality to Quantum Chromodynamics (QCD) at zero chemical potential. The research leverages the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence as a framework to provide insights into the thermodynamic properties of finite temperature QCD through a novel approach that shifts away from conformal invariance.

Overview

In this paper, the authors propose using suitable classes of black holes as gravity duals to gauge theories, breaking the conformal symmetry to better emulate the thermodynamic behavior of QCD over a broad temperature range. The paper considers several potential constructions for five-dimensional gravity models that include Lorentz-invariant actions with non-conformal field components, providing various computations and predictions.

Numerical Results and Observations

• Thermodynamic Properties: The paper showcases a class of translationally invariant black hole solutions with equations of state that closely align with QCD plasma, for which the authors compute the bulk viscosity to entropy density ratio, $\zeta/s$. For black hole constructions that exhibit a first-order phase transition, a sharp rise in $\zeta/s$ near the critical temperature $T_c$ is reported. In contrast, constructions with a smooth cross-over show a modest increase.
• Equation of State and Speed of Sound: The authors contextualize their symmetries using the example of the AdS/Schwarzschild solution but elaborate for results beyond the asymptotically AdS framework. The speed of sound, $c_s^2$, is computed using the temperature-to-entropy relationship, adapting potentials like $V(\phi) = {-12 \cosh{\gamma \phi} + b \phi^2}/L^2$, that provide numerical alignments with lattice-derived thermal QCD.

Analytical Methods and Techniques

The methodology relies heavily on varying the parameters and structure of the potential $V(\phi)$. For instance, the potential structure influences the thermodynamic trajectory and the behavior of bulk viscosity, specifically near phase transitions. Equation modifications like the introduction of additional quadratic and quartic terms are demonstrated to impact $c_s^2$ and potential shape, indicating nuanced correlations between potential expansions and thermodynamic stability.

Implications and Speculative Developments

In theoretical and practical terms, the implications are significant for understanding QCD behavior under finite temperature conditions. The results demonstrate continuity within the analog model and suggest further inquiry into extendability and constraint matching. Potential developments could involve exploring the dynamic range for holographic approximations further into the confinement phase, refining the scalar field potential approximation, and engaging in comparative studies with sophisticated lattice QCD models for QCD with multiple flavors.

The paper’s investigations highlight how a deeper understanding of gravitational duals, particularly with complex, dynamically tuned potential fields, can pioneer more refined holographic correspondences for non-conformal gauge theories. There remains an intriguing opportunity to align further these insights with experimental QCD values, potentially guiding experimental focus and refining theoretical modeling in quantum field theory and thermodynamics.