Topological term and non-peruturbative fluctuations

拓扑学有望在QCD动力学中发挥重要作用。研究拓扑项的非摄动性是一个重要的问题。本文采用蒙特卡罗模拟的方法研究了带拓扑项的CP （N-1）模型。为了模拟复玻兹曼权值，我们采用了一种测量拓扑电荷分布P (Q)的方法。这种方法在某些情况下产生了自由能作为函数的平坦化行为。我们发现平坦化归因于计算P (Q)时的错误。为了研究连续体特征，我们还计算了具有不动点作用的CP （N-1）模型。对于CP(3)情况，P (Q)、自由能和相关长度表现出很好的标度行为。

Topology is expected to play an important role in the dynamics of QCD. It is an important issue to study non-perturbatively a topological term. In this research, we study CP (N-1) model with topological term by means of Monte Carlo simulations. In order to perform simulations for the complex Bo1tzmann weight, we adopt a method by which topological charge distribution P (Q) is measured.This method produces in some cases the flattening behaviors of the free energy as a function of theta. We find that the flattening is attributed to errors in calculating P (Q). We also compute the CP (N-1) model with fixed point action in order to study the continuum feature.For CP (3) case, P (Q), free energy and correlation lengths show very nice scaling behaviors.