What can super-YM theory teach us about thermal QCD ?

The AdS/CFT duality has allowed theorists to calculate previously incalculable quantities in a strongly coupled gauge theory (see the Review in this VJ), albeit one with infinitely many colors. However, the theoretical magic comes at a price: The (N=4) super-Yang Mills (SYM) theory is conformally invariant while QCD has an intrinsic scale, which allows it to be simultaneous confining at long distances and weakly coupled at short distances. The strongly coupled SYM theory, in its purest form, has neither of these properties. What are the phenomenological consequences of this difference between the two theories with regard to quantities of interest to relativistic heavy ion physics?

To address this question, Liu, Rajagopal, and Shi have recently performed a systematic study that throws new light on the physics governing transport processes in the SYM plasma. To be fair to the SYM theory, they have modified its infrared properties by introducing a scale into the AdS5 metric. This modification breaks conformal invariance at large scales, but leaves it intact at short distances. As a consequence, the theory looks more “QCD-like” at long distances, but remains strongly coupled at (arbitrarily) small scales. This approach has been widely employed to calculate observables in the SYM theory that are of potential interest to relativistic heavy ion physics.

Liu et al. focused on five quantities associated with the passage of fast color charges through the thermal medium: the jet quenching parameter q-hat, the velocity dependence of the color screening length, and the drag coefficient as well as the transverse and longitudinal momentum diffusion coefficients for a heavy quark pulled through the plasma. When they calculated the dependence of these quantities on the conformal symmetry breaking scale and – with the exception of the jet quenching parameter, which is only defined on the light cone – on the velocity v of the moving color charge, they found that only the jet quenching parameter retains a dependence on the infrared scale in the ultrarelativistic limit vc. Their result shows that, as the velocity of the color charge approaches the speed of light, all other quantities probe only ultraviolet properties of the thermal plasma, which remain strongly coupled and unaffected by the conformal symmetry breaking.

Their results imply that any application of the modified SYM theory as a model of thermal QCD must be viewed with caution: ultraviolet freedom dictates that short-distance physics in thermal QCD is governed by weak coupling and thus is very much unlike the physics of the currently available models based on the AdS/CFT duality. The sensitivity of many transport properties in the SYM theory on (strongly coupled) short-distance properties of the thermal plasma can be qualitatively understood in the picture developed by Shuryak and Zahed, where the plasma is composed of arbitrarily tightly bound, colored composite states of the fundamental quanta. A faster and faster moving color charge resolves more and more of these tightly bound states, which are unaffected by the infrared symmetry breaking scale. This is obviously very different from the physics of a thermal QCD plasma.

It would be interesting to understand how the jet quenching parameter escapes this predicament. However, even in this case caution is appropriate when making a comparison with QCD. The jet quenching parameter of a thermal QCD medium should grow logarithmically with the jet energy, because the leading parton can resolve more and more partons of the thermal medium, and thus should not have a finite limit for vc. More complete insight into the physics described by the jet quenching parameter in the SYM theory will probably require a connection with the description of hard processes in the dual gravity model (see separate post).

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