Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models
Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models
复制标题
二维 ℂPN − 1 模型中的 Bion 非微扰贡献与红外重正子
DOI：
10.1007/jhep02(2019)190
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发表时间：
2019
影响因子：
5.4
通讯作者：
N. Sakai
中科院分区：
文献类型：
--
作者：
T. Fujimori;S. Kamata;T. Misumi;M. Nitta;N. Sakai
我们导出了具有扭曲边界条件的二维π × S1上的π PN − 1 σ模型中真实的和复Bions的半经典贡献. bion组态是复化的欧几里德作用量的鞍点，可以看作是一对具有相反拓扑荷的分数瞬子的束缚态。我们首先通过求解模型中的运动方程来推导出bion解，该模型具有模拟NPN − 1量子力学中费米子诱导的相互作用的势。的bion解决方案有准模参数对应的相对距离和相位之间的组成分数瞬子。通过对双子背景下量子涨落的Kaluza-Klein模求和，我们发现准模参数的有效作用量被重正化，并成为动力学尺度（或重正化耦合常数）的函数。在重整化有效作用量的基础上，利用Lefschetz套管方法得到了弱耦合极限下的半经典双子贡献。我们发现，在超对称的情况下，生物子的贡献消失，从超对称性的预期。在非超对称的情况下，非微扰的贡献有一个虚模糊度，这是符合预期的红外renormalon模糊。我们的结果明确地表明，复杂的bion可以解释红外renormalon。
We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP N− 1 sigma model on ℝ× S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂP N− 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.