Mixed RG flows and hydrodynamics at finite holographic screen

We consider a strongly interacting gauge theory at finite temperature and chemical potential and study renormalization group flows of transport coefficients in the framework of gauge/gravity duality. We first study them using the flow equations and compare the results with hydrodynamic results by calculating the Green functions on the arbitrary slice. Two results match exactly. Transport coefficients at arbitrary scale are obtained by calculating hydrodynamics Green functions. When either momentum or charge vanishes, transport coefficients decouple from each other.