Hydrodynamics from scalar black branes

In this paper, using the Gauge/gravity duality techniques, we explore the hydrodynamic regime of a very special class of strongly coupled QFTs that come up with an emerging UV length scale in the presence of a negative hyperscaling violating exponent. The dual gravitational counterpart for these QFTs consists of scalar dressed black brane solutions of exactly integrable Einstein-scalar gravity model with Domain Wall (DW) asymptotics. In the first part of our analysis we compute the $R$-charge diffusion for the boundary theory and find that (unlike the case for the pure $AdS_{4}$ black branes) it scales quite non trivially with the temperature. In the second part of our analysis, we compute the $\eta/s$ ratio both in the non extremal as well as in the extremal limit of these special class of gauge theories and it turns out to be eqaul to $1/4\pi$ in both the cases. These results therefore suggest that the quantum critical systems in the presence of (negative) hyperscaling violation at UV, might fall under a separate universality class as compared to those conventional quantum critical systems with the usual $AdS_4$ duals.