Dimensional Reduction, Seiberg--Witten Map and Supersymmetry

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.

14 pages. One Ref. added. To appear in PRD

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• String Theory and Noncommutative Geometry
• Non(anti)commutative Superspace
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Cited by in corpus (5)

• Seiberg--Witten Maps to All Orders
• Pauli Oscillator In Noncommutative Space
• On the All Order Solutions of Seiberg-Witten Map for Noncommutative Gauge Theories
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly