Robustness and Infrared Sensitivity of Various Observables in the Application of AdS/CFT to Heavy Ion Collisions

We investigate the robustness with respect to the introduction of nonconformality of five properties of strongly coupled plasmas that have been calculated in N = 4 supersymmetric Yang-Mills (SYM) theory at nonzero temperature, motivated by the goal of understanding phenomena in relativistic heavy ion collisions. (The five properties are the jet quenching parameter, the velocity dependence of screening, and the drag and transverse and longitudinal momentum diffusion coefficients for a heavy quark pulled through the plasma.) We do so using a toy model in which nonconformality is introduced via a one-parameter deformation of the AdS black hole dual to the hot N = 4 SYM plasma. For values of this parameter which correspond to a degree of nonconformality comparable to that seen in lattice calculations of QCD thermodynamics at temperatures a few times that of the crossover to quark-gluon plasma, we find that the jet quenching parameter is affected by the nonconformality at the 30% level or less, the screening length is affected at the 20% level or less, but the drag and diffusion coefficients for a slowly moving heavy quark can be modified by as much as 80%. However, we show that all but one of the five properties that we investigate become completely insensitive to the nonconformality in the high velocity limit v → 1. The exception is the jet quenching parameter, which is unique among the quantities that we investigate in being “infrared sensitive” even at v = 1, where it is defined. That is, it is the only high-velocity observable that we investigate which is sensitive to properties of the medium at infrared energy scales proportional to T , namely the scales where the quark-gluon plasma of QCD can be strongly coupled. The other four quantities all probe only scales that are larger than T by a factor that diverges as v → 1, namely scales where the N = 4 SYM plasma can be strongly coupled but the quark-gluon plasma of QCD is not.