Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model

TL;DR

This paper explores non-perturbative saddle points in the principal chiral model, revealing fractons and unitons, and demonstrating their roles in mass gap generation and IR renormalons through resurgence theory.

Contribution

It introduces new fracton saddle points and provides a quantum interpretation of unitons, advancing understanding of non-perturbative effects in theories without instantons.

Findings

Discovery of fracton saddle points in PCM.

Quantum interpretation of unitons as unstable solutions.

Fractons explain IR renormalons and mass gap formation.

Abstract

We explain the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, which unifies perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we find new non-perturbative `fracton' saddle point field configurations, and give a quantum interpretation of previously discovered `uniton' unstable classical solutions. The fractons lead to a semi-classical realization of IR renormalons in the circle-compactified theory, and yield the microscopic mechanism of the mass gap of the PCM.