Edge States from Defects on the Noncommutative Plane

Details Edge States from Defects on the Noncommutative Plane Edge States from Defects on the Noncommutative Plane

2003-07-23

arxiv.org/abs/hep-th/0307234v2

Mod.Phys.Lett. A18 (2003) 2509-2516

Physics

High Energy Physics

High Energy Physics - Theory

9 pages; Talk presented by at the conference ``Space-time and Fundamental Interactions: Quantum Aspects'' in honor of A.P. Bal

Scientific paper

10.1142/S0217732303012751

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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