Resummation and renormalons in a general Quantum Field Theory

TL;DR

This paper extends the concepts of Borel resummability and renormalons to complex quantum field theories with multiple fields and couplings, providing methods to identify resummable regions and illustrating with a two-field toy model.

Contribution

It introduces a generalized approach to analyze renormalons and resummability in multi-field quantum field theories, expanding beyond single-field cases.

Findings

Analytic solutions to multi-field RG equations enable renormalon identification.

Methods to determine resummable regions in coupling space are developed.

Illustration with a two-field toy model demonstrates the approach.

Abstract

We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the renormalons is provided by exploiting an analytic solution of the generic one-loop renormalization group equations in multi-field theories. Methods to evaluate the regions in coupling space where the theory is resummable are described. The generalization is then illustrated in a toy model with two coupled scalar fields, representing the simplest extension of the one-field analysis presented in the seminal works of the subject. Furthermore, possible links to realistic theories are briefly discussed.