On the Connection Between 2d Topological Gravity and the Reduced Hermitian Matrix Model

TL;DR

This paper explores the relationship between 2d topological gravity and the reduced Hermitian matrix model, providing a detailed genus-zero mapping and solving the planar graph counting problem with even vertices.

Contribution

It introduces a detailed genus-zero mapping between 2d topological gravity and the reduced Hermitian matrix model, solving the planar graph enumeration problem.

Findings

Complete solution to planar graph counting with even vertices

Mapping between matrix models and topological gravity at genus zero

Analysis of multi-critical models and gravity connection

Abstract

We discuss how concepts such as geodesic length and the volume of space-time can appear in 2d topological gravity. We then construct a detailed mapping between the reduced Hermitian matrix model and 2d topological gravity at genus zero. This leads to a complete solution of the counting problem for planar graphs with vertices of even coordination number. The connection between multi-critical matrix models and multi-critical topological gravity at genus zero is studied in some detail.