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Seiberg-Witten map for noncommutative super Yang-Mills theory

V. Putz·R. Wulkenhaar
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Abstract

In this letter we derive the Seiberg-Witten map for noncommutative super Yang-Mills theory in Wess-Zumino gauge. Following (and using results of) hep-th/0108045 we split the observer Lorentz transformations into a covariant particle Lorentz transformation and a remainder which gives directly the Seiberg-Witten differential equations. These differential equations lead to a theta-expansion of the noncommutative super Yang-Mills action which is invariant under commutative gauge transformations and commutative observer Lorentz transformation, but not invariant under commutative supersymmetry transformations: The theta-expansion of noncommutative supersymmetry leads to a theta-dependent symmetry transformation. For this reason the Seiberg-Witten map of super Yang-Mills theory cannot be expressed in terms of superfields.

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V. Putz, R. Wulkenhaar. 2002-12-11. Seiberg-Witten map for noncommutative super Yang-Mills theory. https://doi.org/10.1142/s0217751x03015246

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