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Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map

We show that the noncommutative Yang-Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The noncommutative Yang-Mills action is invariant under combined conformal transformations of the Yang-Mills field and of the noncommutativity parameter θ. The Seiberg-Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action.

preprint2001arXivOpen access
A. A. BichlJ. M. GrimstrupH. GrosseE. KrausL. PoppM. SchwedaR. Wulkenhaar
hep-th
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A. A. BichlJ. M. GrimstrupH. GrosseE. KrausL. PoppM. SchwedaR. Wulkenhaar

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