Effective Potential in Finite Formulation of QFT

TL;DR

This paper demonstrates a divergence-free method for calculating the quantum effective potential in perturbative QFT, effectively handling hierarchies between fields without fine-tuning.

Contribution

It extends a divergence-free approach to compute the quantum effective potential, avoiding intermediate divergences and fine-tuning in theories with hierarchical vevs.

Findings

Effective potential computed without divergences

Hierarchy between field vevs maintained without fine-tuning

Method applicable to multi-field theories

Abstract

In recent works, we have shown how $n$-point correlation functions in perturbative QFT can be computed without running into intermediate divergences. Here we want to illustrate explicitly that one can calculate the quantum effective potential by the same method. As a main example, we consider a theory with two fields having large and small vacuum expectation values (vev). We show that no fine-tuning between the {\it physical quantities} is needed to keep the hierarchy between the vevs of different fields.