论文标题
朝着Sigma模型中的Lefschetz Thimbles，I
Towards Lefschetz thimbles in Sigma models, I
论文作者
论文摘要
我们研究了二维路径积分lefschetz Thimbles，即可能的路径积分轮廓。具体而言，在$ O（n）$和$ {\ bf cp}^{n-1} $模型的示例中，我们找到了Sigma模型动作的一大批复杂临界点，这些操作在有限温度下与该理论相关，在有限的体积中，具有各种化学势与模型符号的各种化学电位。在本文中，我们讨论了$ O（2M）$和$ {\ bf cp}^{n-1} $模型在零instanton Charge的范围内，以及$ O（2M+1）$模型的某些解决方案。 $ {\ bf cp}^{n-1} $ - 所有Instanton费用的型号和$ o（n）$ - 具有奇数$ n $的$ o（n）$的更通用解决方案，将在即将发表的论文中进行讨论。
We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the $O(N)$ and ${\bf CP}^{N-1}$ models, we find a large class of complex critical points of the sigma model actions which are relevant for the theory in finite volume at finite temperature, with various chemical potentials corresponding to the symmetries of the models. In this paper we discuss the case of the $O(2m)$ and the ${\bf CP}^{N-1}$ models in the sector of zero instanton charge, as well as some solutions of the $O(2m+1)$ model. The ${\bf CP}^{N-1}$-model for all instanton charges and a more general class of solutions of the $O(N)$-model with odd $N$ will be discussed in the forthcoming paper.
