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

Expectation values of Wilson loops define the nonperturbative properties ofthe hot medium produced in heavy ion collisions that arise in the analysis ofboth radiative parton energy loss and quarkonium suppression. We use theAdS/CFT correspondence to calculate the expectation values of such Wilson loopsin the strongly coupled plasma of N=4 super Yang-Mills (SYM) theory, allowingfor the possibility that the plasma may be moving with some collective flowvelocity as is the case in heavy ion collisions. We obtain the N=4 SYM valuesof the jet quenching parameter $\hat q$, which describes the energy loss of ahard parton in QCD, and of the velocity-dependence of the quark-antiquarkscreening length for a moving dipole as a function of the angle between itsvelocity and its orientation. We show that if the quark-gluon plasma is flowingwith velocity v_f at an angle theta with respect to the trajectory of a hardparton, the jet quenching parameter $\hat q$ is modified by a factorgamma_f(1-v_f cos theta), and show that this result applies in QCD as in N=4SYM. We discuss the relevance of the lessons we are learning from all thesecalculations to heavy ion collisions at RHIC and at the LHC. Furthermore, wediscuss the relation between our results and those obtained in other theorieswith gravity duals, showing in particular that the ratio between $\hat q$ inany two conformal theories with gravity duals is the square root of the ratioof their central charges. This leads us to conjecture that in nonconformaltheories $\hat q$ defines a quantity that always decreases alongrenormalization 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.Comment: 61 pages, 8 figures. Note added discussing relation between our work and that in several papers that have appeared recently. References adde