KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model

TL;DR

This paper introduces a new family of KP tau-functions derived from a deformation of the generalized Kontsevich matrix model, connecting to cubic Hodge integrals and higher spin cases.

Contribution

It presents a novel family of KP tau-functions linked to a deformed matrix model, extending the understanding of Hodge integrals and their generalizations.

Findings

The simplest family member encodes cubic Hodge integrals satisfying Calabi-Yau conditions.

The entire family generalizes to higher spin cases.

A new Sato Grassmannian description via Kac-Schwarz operators is developed.

Abstract

In this paper we introduce a new family of the KP tau-functions. This family can be described by a deformation of the generalized Kontsevich matrix model. We prove that the simplest representative of this family describes a generating function of the cubic Hodge integrals satisfying the Calabi-Yau condition, and claim that the whole family describes its generalization for the higher spin cases. To investigate this family we construct a new description of the Sato Grassmannian in terms of a canonical pair of the Kac-Schwarz operators.