Heavy flavor diffusion in weakly coupled N = 4 Super Yang - Mills theory

We use perturbation theory to compute the diffusion coefficient of a heavy quark or scalar moving in N = 4 SU(Nc) Super Yang-Mills plasma to leading order in the coupling and the ratio T/M ≪ 1. The result is compared both to recent strong coupling calculations in the same theory and to the corresponding weak coupling result in QCD. This way, we obtain an estimate for the heavy quark diffusion coefficient in QCD at αs = 0.5 that is consistent with the one made by Moore and Teaney. Finally, we present a compact and simple formulation of the Lagrangian of our theory, N = 4 SYM coupled to a massive fundamental N = 2 hypermultiplet, which is well-suited for weak coupling expansions.