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

Understand

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.