标题： 格点研究关于在 ${\mathbb R}\times S^{1}$ 上的扭曲 ${\mathbb C}P^{N-1}$ 模型 显示英文标题

标题： Lattice study on the twisted ${\mathbb C}P^{N-1}$ models on ${\mathbb R}\times S^{1}$

摘要： 我们报告了在$S_{s}^{1}$(大)$\times$ $S_{\tau}^{1}$ (小) 上的${\mathbb C} P^{N-1}$西格玛模型的格点模拟结果。 我们取足够大的周长比值来近似模型在${\mathbb R} \times S^1$上的情况。 对于在$S_{\tau}^{1}$方向上施加周期性边界条件，我们表明聚变环的期望值在紧致化周长减小时会发生禁闭交叉，其中相关顺磁率的峰值随着$N$的增大而变得更尖锐。 对于${\mathbb Z}_{N}$的扭曲边界条件，我们发现，即使在相对较高的$\beta$（小周长）情况下，普拉科夫环的正$N$边形分布会导致普拉科夫环的小期望值，这表明如果采用足够的统计量和大体积，将意味着未破缺的${\mathbb Z}_{N}$对称性。 我们还通过研究普拉科夫环对$S_{s}^{1}$方向的依赖性，论证了分数瞬子和双子的存在，这会导致${\mathbb Z}_{N}$真空之间的转变。 显示英文摘要

摘要： We report the results of the lattice simulation of the ${\mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $\times$ $S_{\tau}^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${\mathbb R} \times S^1$. For periodic boundary condition imposed in the $S_{\tau}^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${\mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $\beta$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${\mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${\mathbb Z}_{N}$ vacua.