Chern-Simons action in noncommutative space
N. Grandi, G.A. Silva
TL;DR
This paper derives the noncommutative Chern-Simons action from Dirac fermions in various representations and demonstrates its relation to the standard action via the Seiberg-Witten map.
Contribution
It provides a derivation of the noncommutative Chern-Simons action for different fermion representations and analyzes its properties and relation to the commutative case.
Findings
Noncommutative Chern-Simons action derived for fundamental, antifundamental, and adjoint representations.
Seiberg-Witten map relates noncommutative and commutative Chern-Simons actions.
Properties of the noncommutative Chern-Simons action discussed.
Abstract
We derive the noncommutative Chern-Simons action induced by Dirac fermions coupled to a background gauge field, for the fundamental, antifundamental, and the adjoint representation. We discuss properties of the noncommutative Chern-Simons action showing in particular that the Seiberg-Witten formula maps it into the standard commutative Chern-Simons action.
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