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

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.

Figures (2)

• Figure 1: Action densities $\mathcal{S}$ for small (left) and large (right) $SU(2)$ unitons in the setting described in the text. The large uniton splits into two fractons.
• Figure 2: Action densities $\mathcal{S}$ for large $SU(3)$ and $SU(4)$ unitons, which split into three and four fractons respectively.