Quantum Hall physics = noncommutative field theory

In this note, we study a matrix-regularized version of non-commutative U(1)Chern-Simons theory proposed recently by Polychronakos. We determine a completeminimal basis of exact wavefunctions for the theory at arbitrary level k andrank N and show that these are in one-to-one correspondence with Laughlin-typewavefunctions describing excitations of a quantum Hall droplet composed of Nelectrons at filling fraction 1/k. The finite matrix Chern-Simons theory isshown to be precisely equivalent to the theory of composite fermions in thelowest Landau level, believed to provide an accurate description of the fillingfraction 1/k fractional quantum Hall state. In the large N limit, this impliesthat level k noncommutative U(1) Chern-Simons theory is equivalent to theLaughlin theory of the filling fraction 1/k quantum Hall fluid, as conjecturedrecently by Susskind.Comment: 17 pages, LaTeX, v2: references and comment adde