Wilson loops in heavy ion collisions and their calculation in AdS/CFT

Abstract

Expectation values of Wilson loops define the nonperturbative properties of the hot medium produced in heavy ion collisions that arise in the analysis of both radiative parton energy loss and quarkonium suppression. We use the AdS/CFT correspondence to calculate the expectation values of such Wilson loops in the strongly coupled plasma of N=4 super Yang-Mills (SYM) theory, allowing for the possibility that the plasma may be moving with some collective flow velocity as is the case in heavy ion collisions. We obtain the N=4 SYM values of the jet quenching parameter $\hat q$, which describes the energy loss of a hard parton in QCD, and of the velocity-dependence of the quark-antiquark screening length for a moving dipole as a function of the angle between its velocity and its orientation. We show that if the quark-gluon plasma is flowing with velocity v_f at an angle theta with respect to the trajectory of a hard parton, the jet quenching parameter $\hat q$ is modified by a factor gamma_f(1-v_f cos theta), and show that this result applies in QCD as in N=4 SYM. We discuss the relevance of the lessons we are learning from all these calculations to heavy ion collisions at RHIC and at the LHC. Furthermore, we discuss the relation between our results and those obtained in other theories with gravity duals, showing in particular that the ratio between $\hat q$ in any two conformal theories with gravity duals is the square root of the ratio of their central charges. This leads us to conjecture that in nonconformal theories $\hat q$ defines a quantity that always decreases along renormalization group trajectories and allows us to use our calculation of $\hat q$ in N=4 SYM to make a conjecture for its value in QCD.