Tales of D0 on D6 Branes: Matrix Mechanics of Identical Particles

TL;DR

This paper develops a matrix model describing the dynamics of identical particles in even-dimensional space, revealing how the moduli space metric governs their interactions and relating it to various physical theories.

Contribution

It introduces a new matrix model for identical particles, derives the moduli space metric for two particles, and connects this model to fractional quantum Hall effect, instantons, and D-branes.

Findings

Particle size scales as √N for tightly packed configurations.

The model's degrees of freedom are proportional to particle number after constraints.

The moduli space metric influences particle dynamics and is explicitly derived for two particles.

Abstract

We investigate a class of matrix model which describes the dynamics of identical particles in even dimentional space. We show that the degrees of freedom after some constraints are implimented is proportional to particle number and consist of those for positions and internal degrees. The particle dynamics is given by the metric on the smooth moduli space. The moduli space metric for two particles is found. The size of tightly packed $N$ particles grows like $\sqrt{N}$. Our matrix model is related to the matrix model for fractional quantum Hall effect, the ADHM formalism of U(1) instantons on noncommutative space, and supersymmetric D0 branes on D6 branes with nonzero B-field in type IIA theory.