标题： 正弦-戈登/三阶皮亚诺 tau 函数的连接问题与不规则共形块 显示英文标题

标题： Connection problem for the sine-Gordon/Painlevé III tau function and irregular conformal blocks

摘要： 径向正弦-高斯/帕莱夫方程的tau函数的短距离展开式由一个收敛级数给出，该级数包含不规则的$c=1$共形块，并且相对于单值数据具有一定的周期性性质。 长距离不规则展开式相对于单值流形上的不同坐标对表现出类似的周期性。 这一观察结果被用来猜想连接常数的精确表达式，该常数提供了两个级数的相对归一化。 除去一个基本因子，它由两组坐标之间的规范变换的生成函数给出。 显示英文摘要

摘要： The short-distance expansion of the tau function of the radial sine-Gordon/Painlev\'e III equation is given by a convergent series which involves irregular $c=1$ conformal blocks and possesses certain periodicity properties with respect to monodromy data. The long-distance irregular expansion exhibits a similar periodicity with respect to a different pair of coordinates on the monodromy manifold. This observation is used to conjecture an exact expression for the connection constant providing relative normalization of the two series. Up to an elementary prefactor, it is given by the generating function of the canonical transformation between the two sets of coordinates.