AI 中文总结
该研究针对带交替边界条件的环带高斯自由场，构造配分函数并证明其满足环带BPZ方程，通过控制配分函数推导出能级线穿越环带的概率。
AI 中文摘要
我们研究带有交替边界条件的环带上高斯自由场（Gaussian free field, GFF）的能级线，计算所有能级线穿越环带的概率，该概率由两个配分函数的比值给出。这两个配分函数通过Dubédat正则化Dirichlet能量构造，我们证明它们是环带Belavin-Polyakov-Zamolodchikov（BPZ）方程的解。环带设定下变量数多于BPZ方程数，仅靠BPZ系统无法唯一确定配分函数，但通过对上述两个配分函数建立充分的控制，我们成功推导出了穿越概率。
英文摘要
We consider level lines of Gaussian free field (GFF) in annulus with alternating boundary conditions. We calculate the probability that all level lines cross the annulus. Such probability is given by the ratio between two partition functions. These two partition functions are constructed via Dubédat's regularized Dirichlet energy. We show that these partition functions are solutions to annulus Belavin-Polyakov-Zamolodchikov (BPZ) equations. In the annulus setup, the number of variables exceeds the number of BPZ equations, so the BPZ system alone does not determine the partition functions uniquely. By establishing sufficiently good control of the two partition functions constructed above, we are nevertheless able to derive the crossing probability.
Comments64 pages, 2 figures
