Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-03-21
JHEP 0110:039,2001
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, LaTeX, v2: references and comment added
Scientific paper
10.1088/1126-6708/2001/10/039
In this note, we study a matrix-regularized version of non-commutative U(1) Chern-Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix Chern-Simons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) Chern-Simons theory is equivalent to the Laughlin theory of the filling fraction 1/k quantum Hall fluid, as conjectured recently by Susskind.
Hellerman Simeon
Raamsdonk Mark Van
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