On Lagrangian description of Borel resummation

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.