Analyticity domain of a Quantum Field Theory and Accelero-summation

TL;DR

This paper explores how acceleration techniques, specifically Ecalle's acceleration, refine the understanding of the analyticity domain in asymptotically free quantum field theories, suggesting a horn-shaped domain consistent with 't Hooft's expectations.

Contribution

It demonstrates that acceleration methods can accurately describe the horn-shaped analyticity domain of quantum field theories, extending beyond standard Borel summation.

Findings

Acceleration yields horn-shaped analyticity domains.

Standard Borel summation provides larger domains.

Acceleration aligns with 't Hooft's analyticity expectations.

Abstract

From 't Hooft's argument, one expects that the analyticity domain of an asymptotically free quantum field theory is horned shaped. In the usual Borel summation, the function is obtained through a Laplace transform and thus has a much larger analyticity domain. However, if the summation process goes through the process called acceleration by Ecalle, one obtains such a horn shaped analyticity domain. We therefore argue that acceleration, which allows to go beyond standard Borel summation, must be an integral part of the toolkit for the study of exactly renormalisable quantum field theories. We sketch how this procedure is working and what are its consequences.