Dimensional Reduction, Seiberg--Witten Map and Supersymmetry

TL;DR

This paper explores how dimensional reduction of the Seiberg-Witten map extends to other fields in gauge theories and develops a method to define deformed supersymmetry transformations that preserve the action.

Contribution

It demonstrates that dimensional reduction of the Seiberg-Witten map applies to all noncommutative fields and introduces a general approach for deformed supersymmetry transformations.

Findings

Derived Seiberg-Witten maps for 6D and 4D theories.

Showed dimensional reduction induces maps for all fields.

Established a method for invariant deformed supersymmetry transformations.

Abstract

It is argued that dimensional reduction of Seiberg-Witten map for a gauge field induces Seiberg-Witten maps for the other noncommutative fields of a gauge invariant theory. We demonstrate this observation by dimensionally reducing the noncommutative N=1 SYM theory in 6 dimensions to obtain noncommutative N=2 SYM in 4 dimensions. We explicitly derive Seiberg-Witten maps of the component fields in 6 and 4 dimensions. Moreover, we give a general method to define the deformed supersymmetry transformations that leaves the actions invariant after performing the Seiberg-Witten maps.