Seiberg–Witten Map for Noncommutative Super Yang–Mills Theory

Abstract

In this paper 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 θ-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 θ-expansion of noncommutative supersymmetry leads to a θ-dependent symmetry transformation. For this reason the Seiberg–Witten map of super Yang–Mills theory cannot be expressed in terms of superfields.