Link between the hierarchical reference theory of liquids and a new version of the non-perturbative renormalization group in statistical field theory

I propose a new derivation 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.-M. Caillol, J. Phys. A : Math. Gen. 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 [A. Parola and L. Reatto, Adv. Phys. 44, 211 (1995)] is recovered for a sharp infrared cut-off of the propagator.