Matrix model for the total descendant potential of a simple singularity of type $D$

TL;DR

This paper develops a Hermitian matrix model for the total descendant potential associated with a simple singularity of type D, paralleling the Kontsevich matrix model for intersection numbers on moduli spaces.

Contribution

It introduces a novel Hermitian matrix model specifically tailored for the type D singularity's descendant potential, expanding matrix model applications in singularity theory.

Findings

Constructed a Hermitian matrix model for type D singularity

Established parallels with the Kontsevich matrix model

Provided a new tool for studying intersection theory in singularity contexts

Abstract

We construct a Hermitian matrix model for the total descendant potential of a simple singularity of type D similar to the Kontsevich matrix model for the generating function of intersection numbers on the Deligne--Mumford moduli spaces $\overline{\mathcal{M}}_{g,n}$.