[Paper Review] The Effect of Vorticity on QGP Thermodynamics

Brett McInnes|arXiv (Cornell University)|Aug 2, 2018

Black Holes and Theoretical Physics42 references4 citations

TL;DR

Using a gauge-gravity holographic model with the recently proposed holographic vorticity bound, this paper demonstrates that vorticity significantly reduces the entropy density to energy density ratio (s/ε) in Quark-Gluon Plasma (QGP) produced in peripheral heavy-ion collisions at low impact energies (e.g., √sNN = 19.6–39 GeV), decreasing it to approximately one-third of the value in central collisions. This effect is dominant over magnetic fields in this energy regime, implying strong modifications to QGP thermodynamics and transport properties such as kinematic viscosity and jet quenching.

ABSTRACT

Currently there is intense interest in the properties of the Quark-Gluon Plasma produced in peripheral collisions of heavy ions at various facilities, such as the RHIC. In particular, it is essential to understand the difference between such plasmas and their more readily understood counterparts produced in nearly central collisions. The differences arise primarily from the intense magnetic and vorticity fields generated in the QGP in the peripheral case. It has been argued that the magnetic fields might have a profound effect on QGP thermodynamics. Here we will argue, using a gauge-gravity model incorporating the recently proposed holographic vorticity bound, that vorticity also has important consequences for the plasma thermodynamics, in particular, for the entropy density at a given impact energy. A crucial point in our analysis is the need to determine the fate of bulk gravitational parameters when the duality translates them to the boundary.

Motivation & Objective

• To investigate whether vorticity in peripheral Quark-Gluon Plasmas (QGP) significantly alters their thermodynamic properties, particularly entropy density, in contrast to central collisions.
• To determine the relative impact of vorticity versus magnetic fields on QGP thermodynamics in the low-energy regime where vorticity is experimentally detectable.
• To apply the holographic vorticity bound within a gauge-gravity duality framework to model the effects of vorticity on QGP thermodynamics, especially in the presence of large baryonic chemical potential.
• To clarify the fate of bulk gravitational parameters—such as angular momentum and charge—when mapped to the boundary theory in holographic models of QGP.
• To assess whether vorticity-induced modifications to s/ε have measurable consequences for QGP transport properties like kinematic viscosity and jet quenching.

Proposed method

• The study employs a gauge-gravity duality model with a rotating, charged black hole in asymptotically AdS space to represent the QGP at finite temperature, baryonic chemical potential, and vorticity.
• The holographic vorticity bound is applied to constrain the maximum possible vorticity ω for given energy density ε and angular momentum density α, ensuring consistency with observational data.
• The model incorporates both baryonic chemical potential (μB) and magnetic field (B) as bulk parameters, with their boundary values derived via the holographic dictionary.
• The entropy density s is computed via the Bekenstein-Hawking formula s = A/4G, where A is the horizon area of the black hole, and s/ε is evaluated for varying impact energies and centralities.
• The analysis compares s/ε in the presence of vorticity (a,0), with and without magnetic fields (a,Bmax/10 and a,Bmax), and against the non-vortical case (0,0) across multiple collision energies.
• The dimensionless parameter ϖ ∝ B∞/μB² is used to quantify the relative strength of the magnetic field, showing it is suppressed at low energies, thus minimizing its influence on s/ε.

Experimental results

Research questions

• RQ1 Does vorticity in peripheral QGP plasmas significantly alter their thermodynamic properties, particularly the entropy density to energy density ratio s/ε, compared to central collisions?
• RQ2 How does the relative strength of vorticity compare to that of magnetic fields in modifying QGP thermodynamics at low impact energies (√sNN ≈ 19.6–39 GeV)?
• RQ3 Can the holographic vorticity bound explain the observed inverse relationship between vorticity and angular momentum-to-energy density ratio (α/ε) in experimental data?
• RQ4 What is the fate of bulk gravitational parameters—such as angular momentum and charge—when mapped to the boundary in holographic models of QGP with vorticity?
• RQ5 To what extent does vorticity dominate over magnetic fields in affecting transport properties like kinematic viscosity and jet quenching in low-energy QGP?

Key findings

• At low impact energies (√sNN = 19.6–39 GeV), the ratio s/ε in vortical QGP is reduced to approximately 0.415, compared to 1.335 in the non-vortical case, indicating a reduction to roughly one-third of the central collision value.
• The s/ε ratio in the presence of vorticity alone (a,0) is consistently around 0.415 across all low-energy cases studied, showing a robust suppression effect due to vorticity.
• Magnetic fields have negligible influence on s/ε in low-energy collisions because the dimensionless ratio B∞/μB² is small, reducing B∞ to effectively zero in the holographic model.
• At high energies (√sNN = 200 GeV), vorticity’s effect diminishes further, with s/ε dropping to 0.399 (a,0) and 0.111 (a,Bmax), indicating magnetic fields dominate in this regime.
• The kinematic viscosity ν = η/ε is significantly reduced in vortical plasmas due to the reduced s/ε ratio, implying altered hydrodynamic flow behavior.
• The results suggest that jet quenching, which depends on entropy density in holographic models, may exhibit unusual behavior in low-energy, highly vortical QGP, particularly in the Beam Energy Scan regime.