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

TL;DR

This paper computes the heavy flavor diffusion coefficient D_Q for a heavy quark or scalar in weakly coupled N=4 SYM plasma at leading order in the coupling and the mass–temperature ratio. Using kinetic theory with elastic 2→2 scattering and static screening, it derives a closed-form expression for D_Q and shows D_Q = D_S. The authors compare the weak-coupling result to strong-coupling AdS/CFT predictions and to Moore–Teaney's QCD result, finding sizable differences at intermediate coupling and a smaller D_Q in SYM at weak coupling. They also present a compact Lagrangian suitable for weak-coupling expansions and discuss future directions, including relativistic diffusion and more QCD-like theories.

Abstract

We use perturbation theory to compute the diffusion coefficient of a heavy quark or scalar moving in N=4 SU(N_c) 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. 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.