Towards 't Hooft parameter corrections to charge transport in strongly-coupled plasma

We study R-charge transport in a wide class of strongly-coupled supersymmetric plasmas at finite temperature with 't Hooft coupling corrections. To achieve this, we use the gauge/string duality and include the full set of order(\alpha'^3) corrections to the supergravity backgrounds given at zeroth order by the direct product of the AdS-Schwarzschild black hole with a five-dimensional compact Einstein manifold. On general grounds, the reduction leads to a large number of higher derivative operators, which we reduce using the symmetries of the solution. We are left with a universal set of operators whose coefficients can in principle be fixed by carrying out an explicit compactification. We apply our results to the computation of the R-charge conductivity of the supersymmetric plasma at finite yet strong coupling.