Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$

Abstract

In this work we study the tau-function $Z^{1D}$ of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of ${\overline{\mathcal{M}}}_{g,n}$. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for $Z^{1D}$; and the second is to use a formula for the connected $n$-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work.

References in corpus (11)

• Hermitean matrix model free energy: Feynman graph technique for all genera
• The spectral curve of the Eynard-Orantin recursion via the Laplace transform
• Emergent Geometry and Mirror Symmetry of A Point
• Counting lattice points in compactified moduli spaces of curves
• A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves
• On Topological 1D Gravity. I
• Hermitian One-Matrix Model and KP Hierarchy
• Genus Expansions of Hermitian One-Matrix Models: Fat Graphs vs. Thin Graphs
• Fat and Thin Emergent Geometries of Hermitian One-Matrix Models
• Grothendieck's Dessins d'Enfants in a Web of Dualities. II
• Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$

Cited by in corpus (1)

• BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions