Seiberg-Witten map for noncommutative super Yang-Mills theory

TL;DR

This paper derives the Seiberg-Witten map for noncommutative super Yang-Mills theory, revealing a theta-expansion that preserves gauge and Lorentz invariance but modifies supersymmetry transformations, indicating the map cannot be expressed via superfields.

Contribution

It provides the explicit Seiberg-Witten map for noncommutative super Yang-Mills theory in Wess-Zumino gauge, highlighting the impact on supersymmetry transformations.

Findings

Theta-expansion preserves gauge invariance.

Theta-expansion breaks supersymmetry invariance.

Seiberg-Witten map cannot be expressed in superfield form.

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.