Abstract
We study classical configurations in the \( \mathbb{C} \) P N −1 model on \( \mathbb{R} \) 1 × 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 (ν = 1/N ) and one fractionalized anti-instanton (ν = −1/N ) at large separations, and exhibit the attractive interaction between the instan-ton 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 ≥ 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.
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Misumi, T., Nitta, M. & Sakai, N. Neutral bions in the \( \mathbb{C} \) P N −1 model. J. High Energ. Phys. 2014, 164 (2014). https://doi.org/10.1007/JHEP06(2014)164
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DOI: https://doi.org/10.1007/JHEP06(2014)164