Absence of the Holographic Principle in Noncommutative Chern-Simons Theory

Abstract

We examine noncommutative Chern-Simons theory on a bounded spatial domain. We argue that upon `turning on' the noncommutativity, the edge observables, which characterized the commutative theory, move into the bulk. We show this to lowest order in the noncommutativity parameter appearing in the Moyal star product. If one includes all orders, the Hamiltonian formulation of the gauge theory ceases to exist, indicating that the Moyal star product must be modified in the presence of a boundary. Alternative descriptions are matrix models. We examine one such model, obtained by a simple truncation of Chern-Simons theory on the noncommutative plane, and express its observables in terms of Wilson lines.

11 pages

References in corpus (3)

• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• On Level Quantization for the Noncommutative Chern-Simons Theory
• Wilson Loop and Dimensional Reduction in Non-Commutative Gauge Theories

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• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
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• Proceedings to the 'Euroconference on Symmetries Beyond the Standard Model', 12. - 17. July 2003, Portoroz, Slovenia (Part 1 of 2)