Borel-Ecalle resummation of a two-point function

TL;DR

This paper demonstrates that the two-point function in the massless Wess-Zumino model is Borel-Ecalle summable by applying resurgence theory and analyzing its Borel transform, providing a rigorous mathematical foundation for its resummation.

Contribution

It applies resurgence theory and Borel-Ecalle resummation to the Wess-Zumino model, establishing the summability of its two-point function and analyzing its asymptotic properties.

Findings

The two-point function is 1-Gevrey.

Its Borel transform is resurgent.

The two-point function is Borel-Ecalle summable.

Abstract

We provide an overview of the tools and techniques of resurgence theory used in the Borel-Ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two point function on a star-shaped domain of a suitable ramified complex plane. This prove that the two point function of the Wess-Zumino model is Borel-Ecalle summable.