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Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2020-06-22 , DOI: 10.1007/s00023-020-00922-4
Massimo Gisonni , Tamara Grava , Giulio Ruzza

We consider the Laguerre partition function and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven in Cunden et al. (Ann. Inst. Henri Poincaré D, to appear) that correlators have a topological expansion in terms of weakly or strictly monotone Hurwitz numbers that can be explicitly computed from our formulae. As a second result, we identify the Laguerre partition function with only positive couplings and a special value of the parameter \(\alpha =-1/2\) with the modified GUE partition function, which has recently been introduced in Dubrovin et al. (Hodge-GUE correspondence and the discrete KdV equation. arXiv:1612.02333) as a generating function for Hodge integrals. This identification provides a direct and new link between monotone Hurwitz numbers and Hodge integrals.



中文翻译:

Laguerre合奏:相关器,Hurwitz数和Hodge积分

我们考虑了Laguerre分区函数,并根据Hahn多项式的乘积,为具有任意跟踪次数的迹线的连通相关器导出了显式生成函数。最近在Cunden等人中得到了证明。(将出现在An。Inst。HenriPoincaréD中),相关器的弱或严格单调Hurwitz数具有拓扑扩展性,可以从我们的公式中明确计算出该值。作为第二个结果,我们确定仅具有正偶合和参数\(\ alpha = -1 / 2 \)的特殊值的Laguerre分区函数具有改良的GUE分区功能,最近在Dubrovin等人中引入了这种功能。(Hodge-GUE对应关系和离散KdV方程。arXiv:1612.02333)作为Hodge积分的生成函数。此标识提供了单调Hurwitz数与Hodge积分之间的直接和新链接。

更新日期:2020-06-22
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