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

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 Ünsal 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 $N\ge 3$. 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.

35 pages, 20 figures. v2: version published in JHEP. v3: typos corrected

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