Non-Wilsonian ultraviolet completion via transseries

TL;DR

This paper explores a novel non-perturbative ultraviolet completion for scalar field theories using transseries, revealing a new fixed point and implications for renormalization and resummation techniques.

Contribution

It introduces a non-Wilsonian UV completion via transseries and analyzes its impact on the renormalization group and resummation methods in scalar models.

Findings

Discovery of a new non-perturbative fixed point for scalar φ^4 model.

Demonstration of a purely non-Wilsonian UV self-completion dependent on an arbitrary constant.

Insights into the decoupling of scalar mass and prescriptions for Borel-Laplace resummation.

Abstract

We study some of the implications for the perturbative renormalization program when augmented with the Borel-Ecalle resummation. We show the emergence of a new kind of non-perturbative fixed point for the scalar $\phi^4$ model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cut-off, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel-Laplace resummation of the renormalons in non-asymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.