Link between New Versions of the Hierarchical Reference Theory of Liquids and of the Non Perturbative Renormalization Group in Statistical Field Theory

I propose a new version of the Hierarchical Reference Theory of liquids. Two formalisms, one in the grand canonical ensemble, the other in the framework of statistical field theory are given in parallel. In the latter the theory is an avatar of a new version of the non perturbative renormalization group (J. Phys. A : Math. Gen. $\mathbf{\text{42}}$, 225004 (2009)). The flow of the Wilsonian action as well as that of the effective average action of Wetterich are derived and a simple relation between the two functionals is established. The standard Hierarchical Reference Theory for liquids ($\mathit{\text{Adv.}}\mathit{\text{Phys.}}$ $\mathbf{\text{44}}$, 211 (1995)) is recovered for a sharp infra-red cut-off of the propagator