Absence of the Holographic Principle in Noncommutative Chern-Simons Theory

Details Absence of the Holographic Principle in Noncommutative Chern-Simons Theory Absence of the Holographic Principle in Noncommutative Chern-Simons Theory

2001-07-20

arxiv.org/abs/hep-th/0107179v2

JHEP 0111:023,2001

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1088/1126-6708/2001/11/023

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.

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