Shear channel correlators from hot charged black holes

We compute numerically the full retarded Green's functions for conserved currents in the shear channel of a (2+1)-dimensional field theory at non-zero temperature and density. This theory is assumed to be holographically dual to a non-extremal, electric Reissner-Nordstr\om AdS4 black hole with planar horizon. Using the holographic description we obtain results for arbitrary frequencies and momenta and survey the detailed structure of these correlators. In particular, we demonstrate the `repulsion' and `clover-leaf crossing' of their poles and stress the importance of the residues at the poles beyond the hydrodynamic regime. As a consistency check, we show that our results agree precisely with existing literature for the appropriate quasinormal frequencies of the bulk theory.