Abstract
In this paper we report on the formulation of the non‐commutative Chern‐Simons (CS) theory where the spatial slice, an infinite strip, is a manifold with boundaries. Our approach involves the formulation of a new finite‐dimensional matrix model which approximates the CS theory on the non‐commmutative strip. This model has a fuzzy edge which becomes the required sharp edge when size of the matrices approaches infinity. The non‐commutative CS theory on the strip is defined by this limiting procedure. The canonical analysis of the matrix theory reveals that there are edge observables in the theory generating a Lie algebra with properties similar to that of a non‐abelian Kac‐Moody algebra. Using some of the results of this analysis we discuss in detail the limit where this matrix model approximates the CS theory on the infinite strip.
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