On Lagrangian description of Borel resummation

TL;DR

This paper introduces a physical interpretation of Borel resummation by defining it at the Lagrangian level, unifying perturbative and non-perturbative techniques through coupling to a complex dilaton field.

Contribution

It proposes a novel Lagrangian-based framework that unifies Borel resummation and BZJ regularization, linking perturbative and non-perturbative methods.

Findings

Reproduces standard Borel resummation in perturbative sector

Reproduces BZJ regularization in non-perturbative sector

Provides a unified physical interpretation of resummation techniques

Abstract

In this paper we will propose a physical interpretation of Borel resummation. We will define Borel transformation on the Lagrangian level. This transformation essentially coincides with coupling the original theory to the non-dynamical complex dilaton field. In the perturbative sector it reproduces standard Borel resummation. In the non-perturbative sector this transformation reproduces Bogomolny--Zinn-Justin(BZJ) regularization. Our approach unifies the perturbative Borel resummation and non-perturbative BZJ procedure.