We generalise a result of Kazarian regarding Kadomtsev–Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting problems or hypergeometric tau‑functions. The proof uses recent results on the relations between hypergeometric tau-functions and topological recursion, as well as the DOSS correspondence between topological recursion and cohomological field theories. As a particular case, we recover the result of Alexandrov of KP integrability for triple Hodge integrals with a Calabi–Yau condition.

中文翻译：

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Hurwitz 型上同调场论的 KP 层级

我们将 Kazarian 关于单个 Hodge 积分的 Kadomtsev–Petviashvili 可积性的结果推广到与 Hurwitz 型计数问题或超几何 tau 函数相关的一般上同调场论。该证明使用了超几何 tau 函数与拓扑递归之间关系的最新结果，以及拓扑递归与上同调场论之间的 DOSS 对应关系。作为一个特殊情况，我们恢复了具有 Calabi-Yau 条件的三重霍奇积分的 KP 可积性的 Alexandrov 结果。