Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model

TL;DR

This paper investigates fractionalized non-self-dual solutions in the CP(N-1) model with twisted boundary conditions, revealing their role as saddle points contributing to the quantum path integral and their relation to renormalons.

Contribution

It introduces and analyzes fractional non-self-dual solutions in the CP(N-1) model, connecting them to resurgence and non-perturbative effects in quantum field theory.

Findings

Solutions have finite, fractional action and topological charge.

These solutions are unstable with negative fluctuation modes.

They contribute imaginary non-perturbative terms to the path integral.

Abstract

We study non-self-dual classical solutions in the CP(N-1) model with Z_N twisted boundary conditions on the spatially compactified cylinder. These solutions have finite, and fractional, classical action and topological charge, and are `unstable' in the sense that the corresponding fluctuation operator has negative modes. We propose a physical interpretation of these solutions as saddle point configurations whose contributions to a resurgent semi-classical analysis of the quantum path integral are imaginary non-perturbative terms which must be cancelled by infrared renormalon terms generated in the perturbative sector.