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The Symmetry Improved Two-Particle-Irreducible (SI2PI) formalism is apowerful tool to calculate the effective potential beyond perturbation theory,whereby infinite sets of selective loop-graph topologies can be resummed in asystematic and consistent manner. In this paper we study theRenormalization-Group (RG) properties of this formalism, by proving for thefirst time a number of new field-theoretic results. First, the RG runnings ofall proper 2PI couplings are found to be UV finite, in the Hartree-Fock andsunset approximations of the 2PI effective action. Second, the SI2PI effectivepotential is exactly RG invariant, in contrast to what happens in the ordinaryOne-Particle-Irreducible (1PI) perturbation theory, where the effectivepotential is RG invariant only up to higher orders. Finally, we show how theeffective potential of an O(2) theory evaluated in the SI2PI framework,appropriately RG improved, can reach a higher level of accuracy, even up to oneorder of magnitude, with respect to the corresponding one obtained in the 1PIformalism.

Exact RG Invariance and Symmetry Improved 2PI Effective Potential