Neutral bions in the CP^{N-1} model for resurgence

TL;DR

This paper investigates neutral bions in the CP^{N-1} model on R^1 x S^1 with twisted boundary conditions, constructing explicit solutions to understand their role in resurgence and infrared renormalons.

Contribution

It introduces an explicit ansatz for neutral bions composed of fractional instantons and anti-instantons, enabling detailed study of their interactions and implications for resurgence.

Findings

Attractive interactions between fractional instantons are confirmed.

The ansatz approximates solutions at large separations effectively.

Results support the role of neutral bions in resurgence phenomena.

Abstract

Classical configurations in the CP^{N-1} model on R^1 x S^1 is studied with twisted boundary conditions. Starting from fractional instantons with the Z_N twisted boundary conditions, we review briefly the relevance of our study to resurgence phenomenon in field theory. We consider primarily configurations composed of multiple fractional instantons, called "neutral bions", which are identified as "perturbative infrared renormalons". We construct an explicit ansatz corresponding to topologically trivial configurations containing one fractional instanton (nu=1/N) and one fractional anti-instanton (nu=-1/N), which is guaranteed to become a solution of field equations asymptotically for large separations. The attractive interactions between the instanton constituents from small to large separations are found to be consistent with the standard separated-instanton calculus. Our results suggest that the ansatz enables us to study bions and the related physics for a wide range of separations. This talk is mainly based on our recent work published in JHEP 1406, 164 (2014) [arXiv:1404.7225 [hep-th]].