论文标题
Grothendieck的Dessins d'Enfants在双重性网络中。 iii
Grothendieck's Dessins d'Enfants in a Web of Dualities. III
论文作者
论文摘要
我们通过Laguerre Unity Ensemble（LUE）的分区函数确定Dessin分区函数。结合了Cunden等人在Goulden等人引入的LUE相关器与严格的单调Hurwitz数字之间的关系所产生的结果，然后我们建立了Dessin Counting与严格的单调Hurwitz数字的联系。我们还引入了DESSIN/LUE分区函数的校正因子，该功能在表明校正后的Dessin/Lue分区函数中起着重要作用。作为应用程序，我们使用Dubrovin和Zhang的方法来计算Dessin相关器。在物理学家的术语中，我们在Dessin计数，广义Penner模型和$ \ Mathbb {p}^1 $ - topogological Sigma模型之间建立了二元性。
We identify the dessin partition function with the partition function of the Laguerre unitary ensemble (LUE). Combined with the result due to Cunden et al on the relationship between the LUE correlators and strictly monotone Hurwitz numbers introduced by Goulden et al, we then establish connection of dessin counting to strictly monotone Hurwitz numbers. We also introduce a correction factor for the dessin/LUE partition function, which plays an important role in showing that the corrected dessin/LUE partition function is a tau-function of the Toda lattice hierarchy. As an application, we use the approach of Dubrovin and Zhang for the computation of the dessin correlators. In physicists' terminology, we establish dualities among dessin counting, generalized Penner model, and $\mathbb{P}^1$-topological sigma model.
