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arXiv · hep-th/0307234

Edge States from Defects on the Noncommutative Plane

A. Pinzul·A. Stern
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Abstract

We illustrate how boundary states are recovered when going from a noncommutative manifold to a commutative one with a boundary. Our example is the noncommutative plane with a defect, whose commutative limit was found to be a punctured plane - so here the boundary is one point. Defects were introduced by removing states from the standard harmonic oscillator Hilbert space. For Chern-Simons theory, the defect acts as a source, which was found to be associated with a nonlinear deformation of the $w_\infty$ algebra. The undeformed $w_\infty$ algebra is recovered in the commutative limit, and here we show that its spatial support is in a tiny region near the puncture.

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A. Pinzul, A. Stern. 2003-09-16. Edge States from Defects on the Noncommutative Plane. https://doi.org/10.1142/s0217732303012751

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