更高的长度-扭曲坐标、广义Heun's opers和扭曲超势
Higher length-twist coordinates, generalized Heun's opers, and twisted superpotentials
摘要：
本文研究了Nekrasov，Rosly和Shatashvili提出的一个方案，该方案将由S类理论得到的有效扭曲超势几何地描述为某些复化长度-扭曲坐标下的生成函数，并将其推广到更高的秩。首先，我们引入了一个更高的秩模拟Fenchel-Nielsen型谱网络的广义Strebel条件。我们发现新的系统的光谱坐标通过阿贝尔化的方法，并认为他们是更高的秩类似物的Nekrasov-Rosly-Shatashvili达布坐标。其次，我们给出了一个明确的参数化的轨迹的opers和确定的生成函数的拉格朗日子簇的高阶达布坐标在一些具体的例子。我们发现，生成函数确实符合已知的有效扭曲超势。最后，我们将Nekrasov，Rosly和Shatashvili的方法与通过精确WKB方法使用量子周期的方法联系起来。
英文摘要：
In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the effective twisted superpotential obtained from a class S theory geometrically as a generating function in terms of certain complexified length-twist coordinates, and extend it to higher rank. First, we introduce a higher rank analogue of Fenchel-Nielsen type spectral networks in terms of a generalized Strebel condition. We find new systems of spectral coordinates through the abelianization method and argue that they are higher rank analogues of the Nekrasov-Rosly-Shatashvili Darboux coordinates. Second, we give an explicit parametrization of the locus of opers and determine the generating functions of this Lagrangian subvariety in terms of the higher rank Darboux coordinates in some specific examples. We find that the generating functions indeed agree with the known effective twisted superpotentials. Last, we relate the approach of Nekrasov, Rosly and Shatashvili to the approach using quantum periods via the exact WKB method.
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