Heavy quark diffusion in strongly coupled N=4 Yang-Mills theory

By J. Casalderrey-Solana, D. Teaney. 2006

423 citations recorded by the source corpus.

We express the heavy quark diffusion coefficient as the temporal variation of a Wilson line along the Schwinger-Keldysh contour. This generalizes the classical formula for diffusion as a force-force correlator to a non-Abelian theory. We use this formula to compute the diffusion coefficient in strongly coupled $\mathcal{N}=4$ Yang-Mills theory by studying the fluctuations of a string in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}_{5}$. The string solution spans the full Kruskal plane and gives access to contour correlations. The diffusion coefficient is $D=2/\sqrt{\ensuremath{\lambda}}\ensuremath{\pi}T$ and is therefore parametrically smaller than momentum diffusion, $\ensuremath{\eta}/(e+p)=1/4\ensuremath{\pi}T$. The quark mass must be much greater than $T\sqrt{\ensuremath{\lambda}}$ in order to treat the quark as a heavy quasiparticle. The result is discussed in the context of the Relativistic Heavy Ion Collider (RHIC) experiments.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5200a14501a32e955a63d9e99813db222268bd45

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In Nuclear and High Energy Physics

1. S. Gubser
2. V. Hubeny
3. M. Rangamani
4. E. Kiritsis
5. R. Myers
6. D. Mateos
7. S. Hartnoll
8. T. Schaefer

Citations in the corpus

• Holographic spectral functions and diffusion constants for fundamental matter (2007, background): “It is only when semiclassical effects are taken into account that the heavy quarks diffuse through the appearance of Hawking radiation from the effective black hole metric induced on the string worldsheet [43].”
• Extraction of heavy-flavor transport coefficients in QCD matter (2018, positive): “The formulation of the HQ diffusion in terms of electric field strength correlators, or equivalently in terms of force-force correlators acting on the heavy quark, turned out to be very useful when calculating the momentum diffusion coefficient in the weak coupling expansion [96] or in AdS/CFT [99].”
• Momentum fluctuations of heavy quarks in the gauge-string duality (2006, methodology): “The drag force calculations [1, 2, 3] result in a relaxation time tD for charm quarks that is in the right ballpark for comparison with data on the nuclear modification factor RAA and the elliptic flow parameter v2 for heavy quarks, as reported most recently by the STAR and PHENIX collaborations in ”
• A Holographic View on Physics out of Equilibrium (2010, methodology): “The first steps to understand the energy loss for probes in plasmas holographically were carried out in the seminal papers [87, 88, 89, 90, 91, 92, 93, 94], by considering the dynamics of probe strings as described above.”
• Holographic melting and related properties of mesons in a quark-gluon plasma (2006, background): “In contrast to the gluonic degrees of freedom, the matter degrees of freedom may still have bound states in this phase.”
• Improved Holographic QCD (2010, background): “A different approach chooses to compute the drag force acting a string whose UV endpoint (representing an infinitely heavy quark) is forced to move with constant velocity v, [9, 11, 12], in the context of N = 4 SYM plasma.”
• Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, positive): “Using holographic duality one finds [289, 290, 291]”
• Holographic meson melting (2006, result): “In fact, several important plasma parameters, most notably the shear viscosity [3] and the energy loss rate of a heavy quark [4] or the jet quenching parameter using light-like Wilson loops [5] have been calculated with stringy AdS-methods and turned out to be in surprisingly good agreement with exp”
• Heavy ions and string theory (2013, background): “First, detailed calculations of stochastic forces can be carried out [130, 132, 133], resulting in diffusion coefficients”
• Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, background): “In the isotropic case, the drag force on a heavy quark in a strongly coupled plasma has been considered in [38, 39, 154, 155, 156, 157, 158, 159, 160], its energy loss through Cherenkov-emission of heavy quarkonium mesons in [161, 162], and jet quenching in [163, 164, 165, 166, 167, 168, 169, 170].”