Symmetry improvement of 3-particle irreducible effective actions for O(N) scalar field theories

Abstract

Field theories are widely used in areas including high energy, cosmology and condensed matter physics. These applications are growing ever more demanding. However, a gap exists between the standard perturbation theory methods (Feynman diagrams) and large scale “black box” Monte Carlo simulations. n-particle irreducible effective actions (nPIEA) are powerful non-perturbative tools which fill the gap by summing certain subsets of Feynman diagrams to infinite order. Unfortunately, many important properties of field theories depend on order-by-order cancellations (e.g. symmetries, gauge invariances, supersymmetries, unitarity, etc.) which are “brittle” under approximations of nPI effective actions. We have extended a method recently developed by Pilaftsis and Teresi[2] which is designed to restore all symmetries in the nPI formalism. Our extension sums more Feynman diagrams and enforces more of the symmetry, and suggests an extension to gauge theories.