Shear viscosity of a relativistic scalar field from functional renormalization

Renormalization group flow equations of the fluid dynamical shear viscosity transport coefficient of a relativistic real scalar field are derived. The flowing effective action contains branch cut contributions to the self energy and interaction vertex in the symmetric phase. We demonstrate how the flow equation method can systematically extend the perturbative resummation schemes. We show that our truncation is in that sense a minimal scheme in which a reliable viscosity coefficient is obtained.