On a Matrix Model of Level Structure

We consider a matrix model composed of three parts: the dimensionally reduced Yang-Mills terms, d = 1 Chern-Simons term and a kinetic term for a bosonic vector field as introduced by Polychronakos recently. The coefficient, κ of the Chern-Simons term is integer, and hence the level structure. We show at the bottom of the YangMills 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 κ/r repulsive potential from each other. We argue the relevant brane configuration to be D0-branes in a D4 after κ of D8’s pass the system. The repulsive potential is identified as an electric potential in D4 theories due to the charge acquirement of D0 particles from the κ of fundamental string ends generated by the Hanany-Witten effect. ∗Electronic correspondence: [email protected]