English

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

Mathematical Physics 2021-09-09 v1 math.MP Exactly Solvable and Integrable Systems

Abstract

In this work we study the tau-function Z1DZ^{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 Mg,n\overline{\mathcal M}_{g,n}. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for Z1DZ^{1D}; and the second is to use a formula for the connected nn-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.

Keywords

Cite

@article{arxiv.2109.03394,
  title  = {Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of $\overline{\mathcal M}_{g,n}$},
  author = {Zhiyuan Wang and Jian Zhou},
  journal= {arXiv preprint arXiv:2109.03394},
  year   = {2021}
}