The 2PI effective theory at next-to-leading order using the functional renormalization group

TL;DR

This paper develops a renormalization group approach to perform 4-loop 2PI calculations in a scalar theory, simplifying the process and enabling extensions to 4PI level calculations that are otherwise infeasible.

Contribution

It introduces a novel RG-based method for 2PI and 4PI calculations, reducing complexity and overcoming limitations of traditional counterterm approaches.

Findings

Successfully performs 4-loop 2PI calculation using RG method

Simplifies the renormalization process with a single bare coupling constant

Proposes extension of method to 4PI level calculations

Abstract

We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which can not be done using any known method by introducing counterterms.