Neutral bions in the C P N − 1 model

We study classical configurations in the CPN−1 model on R1 × S1 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 ZN 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 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-ZN 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 ZN twisted boundary conditions.