Topological recursion for Kadomtsev–Petviashvili tau functions of hypergeometric type

IF 1 2区 数学 Q1 MATHEMATICS
Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin
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引用次数: 0

Abstract

We study the n $n$ -point differentials corresponding to Kadomtsev–Petviashvili (KP) tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their 2 $\hbar ^2$ -deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov–Scherbin partition functions that do satisfy the natural analytic assumptions, and for these families, we prove in addition the so-called projection property and thus the full statement of the Chekhov–Eynard–Orantin topological recursion. A particular feature of our argument is that it clarifies completely the role of 2 $\hbar ^2$ -deformations of the Orlov–Scherbin parameters for the partition functions, whose necessity was known from a variety of earlier obtained results in this direction but never properly understood in the context of topological recursion. As special cases of the results of this paper, one recovers new and uniform proofs of the topological recursion to all previously studied cases of enumerative problems related to weighted double Hurwitz numbers. By virtue of topological recursion and the Grothendieck–Riemann–Roch formula, this, in turn, gives new and uniform proofs of almost all Ekedahl–Lando–Shapiro–Vainshtein (ELSV)-type formulas discussed in the literature.

超几何型卡多姆采夫-彼得维亚什维利陶函数的拓扑递归
我们研究与超几何型卡多姆采夫-彼得维亚什维利(KP)陶函数(又称奥尔洛夫-舍尔宾分割函数)相对应的 n $n$ 点微分,重点是它们的 ℏ 2 $\hbar ^2$ 变形和展开。在自然所需的分析假设下,我们证明了某些更高的循环方程,其中尤其包含标准的线性和二次循环方程,从而暗示了绽放拓扑递归。我们还区分了两个确实满足自然解析假设的奥尔洛夫-舍宾分割函数大家族,对于这些大家族,我们还证明了所谓的投影性质,从而证明了契科夫-艾纳德-奥兰汀拓扑递归的完整陈述。我们论证的一个特别之处在于,它完全澄清了分割函数的奥尔洛夫-舍宾参数的ℏ 2 $\hbar ^2$变形的作用,我们从早先在此方向上获得的各种结果中知道了其必要性,但从未在拓扑递归的背景下正确理解过。作为本文结果的特例,我们对以前研究过的所有与加权双赫尔维茨数有关的枚举问题的拓扑递归进行了新的统一证明。凭借拓扑递归和格罗thendieck-Riemann-Roch 公式,这反过来又给出了文献中讨论的几乎所有 Ekedahl-Lando-Shapiro-Vainshtein (ELSV) 类型公式的新的统一证明。
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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
186
审稿时长
6-12 weeks
期刊介绍: The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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