Coupling dependence of jet quenching in hot strongly-coupled gauge theories

Previous top-down studies of jet stopping in strongly-coupled QCD-like plasmas with gravity duals have been in the infinite 't Hooft coupling limit lambda -> infinity. They have found that, though a wide range of jet stopping distances are possible depending on initial conditions, the maximum jet stopping distance l(max) scales with energy as E-1/3 at large energy. But it has always been unclear whether the large-coupling and high-energy limits commute. In this paper, we use the string alpha' expansion in AdS-CFT to study the corrections to the lambda=infinity result in powers of 1/lambda. For the particular type of "jets" that we study, we find that (i) the naive expansion in 1/lambda breaks down for certain initial conditions but (ii) the relative corrections to the maximum, stopping distance are small when 1/lambda is small. More specifically, we find that the expansion in 1/lambda is well behaved for jets whose stopping distance l(stop) is in the range lambda(-1/6lmax) << l(stop) less than or similar to l(max), but the expansion breaks down (and the fate of lambda=infinity results is uncertain) for jets created in such a way that l(stop) << lambda(-1/6)l(max). The analysis requires assessing the effects of all higher-derivative corrections to the supergravity action for the gravity dual.