Neutral bions in the ${\mathbb C}P^{N-1}$ model

TL;DR

This paper investigates neutral bion configurations in the ${ m extbf{C}P^{N-1}}$ model on ${ m extbf{R}^1 imes S^1}$ with twisted boundary conditions, analyzing their interactions and implications for infrared renormalons.

Contribution

It introduces explicit ansatze for neutral bions under various twisted boundary conditions and demonstrates their interaction potentials across different separations and N.

Findings

Interaction potential matches separated-instanton calculus.

Ansatz applicable from short to large separations.

Qualitative similarity of bion behavior across boundary conditions.

Abstract

We study classical configurations in the ${\mathbb C}P^{N-1}$ model on ${\mathbb R}^{1}\times S^{1}$ with twisted boundary conditions. We focus on specific configurations composed of multiple fractionalized-instantons, termed "neutral bions", which are identified as "perturbative infrared renormalons" by \"{U}nsal and his collaborators. For ${\mathbb Z}_N$ twisted boundary conditions, we consider an explicit ansatz corresponding to topologically trivial configurations containing one fractionalized instanton ($\nu=1/N$) and one fractionalized anti-instanton ($\nu=-1/N$) at large separations, and exhibit the attractive interaction between the instanton constituents and how they behave at shorter separations. We show that the bosonic interaction potential between the constituents as a function of both the separation and $N$ is consistent with the standard separated-instanton calculus even from short to large separations, which indicates that the ansatz enables us to study bions and the related physics for a wide range of separations. We also propose different bion ansatze in a certain non-${\mathbb Z}_{N}$ twisted boundary condition corresponding to the "split" vacuum for $N= 3$ and its extensions for $N\geq 3$. We find that the interaction potential has qualitatively the same asymptotic behavior and $N$-dependence as those of bions for ${\mathbb Z}_{N}$ twisted boundary conditions.