D-particles, Matrix Integrals and KP hierachy

TL;DR

This paper explores the connection between matrix models describing D-particles and the KP hierarchy, revealing new insights into their correlation functions, coupling dependence, and integrable structure, including a novel derivation of large-N limits.

Contribution

It demonstrates that the partition function of a specific matrix model related to D-particles is a tau-function of the KP hierarchy and provides a new derivation of large-N and double-scaling limits.

Findings

Partition function is a tau-function of KP hierarchy.

Identifies strong/weak 't Hooft coupling dependence.

Provides a new derivation of large-N and double-scaling limits.

Abstract

We study the regularized correlation functions of the light-like coordinate operators in the reduction to zero dimensions of the matrix model describing $D$-particles in four dimensions. We investigate in great detail the related matrix model originally proposed and solved in the planar limit by J. Hoppe. It also gives the solution of the problem of 3-coloring of planar graphs. We find interesting strong/weak 't Hooft coupling dependence. The partition function of the grand canonical ensemble turns out to be a tau-function of KP hierarchy. As an illustration of the method we present a new derivation of the large-N and double-scaling limits of the one-matrix model with cubic potential.