On a Matrix Model of Level Structure

TL;DR

This paper extends a matrix model of D0-branes by incorporating a Chern-Simons term and vector interactions, revealing a linear arrangement of particles and a level structure tied to an integer coefficient, with implications for brane configurations.

Contribution

It introduces a generalized matrix model with a Chern-Simons term, demonstrating a level structure and analyzing the low-energy linear configuration of D0-branes.

Findings

Particles align on a straight line at low energy

The Chern-Simons coefficient must be an integer

D0-branes in a D4 with passing D8-branes are relevant configurations

Abstract

We generalize the dimensionally reduced Yang-Mills matrix model by adding d=1 Chern-Simons term and terms for a bosonic vector. The coefficient, \kappa of the Chern-Simons term must be integer, and hence the level structure. We show at the bottom of the Yang-Mills potential, the low energy limit, only the linear motion is allowed for D0 particles. Namely all the particles align themselves on a single straight line subject to \kappa^2/r^2 repulsive potential from each other. We argue the relevant brane configuration to be D0-branes in a D4 after \kappa of D8's pass the system.