Vertex functions and their flow equations from the 2PI effective action

TL;DR

This paper develops a method to extract n-point vertex functions from the 2PI effective action, extending an alternative functional renormalization group approach from zero to higher dimensions, and clarifying their relationship.

Contribution

It introduces a procedure for deriving vertex functions from the 2PI effective action applicable in higher dimensions, enhancing the functional renormalization group methodology.

Findings

Procedure for extracting vertex functions from 2PI effective action

Extension of the approach from zero to higher dimensions

Clarification of flow equations for couplings and vertices

Abstract

By exploiting the convexity of the two-particle-irreducible (2PI) effective action, we describe a procedure for extracting n-point vertex functions. This procedure is developed within the context of a zero-dimensional "quantum field theory" and subsequently extended to higher dimensions. These results extend the practicability and utility of a recent, alternative approach to the functional renormalization group programme [see arXiv:1907.06503; arXiv:2107.12914], and clarify the relationship between the flow equations for coupling parameters and vertices.