Quantum Hall Physics Equals Noncommutive 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 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 1k quantum Hall fluid, as conjectured recently by Susskind.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research (ER) (US)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 787180
- Report Number(s):
- SLAC-PUB-8796; TRN: US0110449
- Resource Relation:
- Other Information: PBD: 9 Aug 2001
- Country of Publication:
- United States
- Language:
- English
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