Non summable Borel $\Phi^{4}$ theory in zero dimensions and the Generalized Borel Transform

TL;DR

This paper introduces the Generalized Borel Transform (GBT) as an effective non-perturbative analytical method for solving the zero-dimensional $\

Contribution

It presents the GBT technique as a novel approach to analyze the $\

Findings

GBT accurately captures non-perturbative contributions

Renormalons are not the genuine source of non-perturbative effects

Analytical solutions agree with large order perturbation theory estimates

Abstract

A new technique named Generalized Borel Transform (GBT) is applied to the generating functional of the $\Phi^{4}$ theory in zero dimensions with degenerate minima. The analytical solution of this function, obtained in the non perturbative regime, is compared with those estimations predicted by large order perturbation theory. It was established that the GBT is a very efficient technique to capture these contributions. On the other hand, renormalons associated to the resummation of those perturbative series were not found to be the genuine source of the non perturbative contributions of this model.