N ov 2 01 4 Neutral bions in the C P N − 1 model
N ov 2 01 4 Neutral bions in the C P N − 1 model
复制标题
N ov 2 01 4 C P N − 1 模型中的中性生物体
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
N. Sakai
中科院分区：
文献类型：
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作者：
T. Misumi;M. Nitta;N. Sakai
我们研究了R1 × S1上CPN−1模型中的经典组态，并给出了扭曲边界条件。我们专注于由多个分数瞬子组成的特定配置，称为“中性生物子”，由Ünsal及其合作者确定为“微扰红外重正子”。对于ZN扭曲边界条件，我们考虑了一个显式的解析式，它对应于在大间距下包含一个分数化瞬子（ν = 1/N）和一个分数化反瞬子（ν = −1/N）的拓扑平凡组态，并展示了瞬子组分之间的吸引相互作用以及它们在较短间距下的行为。我们发现，玻色子的相互作用势的成分之间的函数的分离和N是一致的标准分离的瞬子演算，即使从短到大的分离，这表明，该分析使我们能够研究bions和相关的物理范围广泛的分离。我们还提出了一种非ZN扭曲边界条件下的不同的双子假设，该边界条件对应于N = 3时的“分裂”真空及其N ≥ 3时的推广。我们发现，在ZN扭曲边界条件下，相互作用势具有与Bions势定性相同的渐近行为和N依赖性。
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.