Seiberg--Witten Maps to All Orders

All order Seiberg--Witten maps of gauge parameter, gauge field and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions as well as by directly solving Seiberg-Witten differential equations. The explicit third order non-abelian and fourth order abelian Seiberg-Witten maps of gauge parameter and gauge field are also presented.Comment: 16 page

Duals of noncommutative supersymmetric U(1) gauge theory

Parent actions for component fields are utilized to derive the dual of supersymmetric U(1) gauge theory in 4 dimensions. Generalization of the Seiberg-Witten map to the component fields of noncommutative supersymmetric U(1) gauge theory is analyzed. Through this transformation we proposed parent actions for noncommutative supersymmetric U(1) gauge theory as generalization of the ordinary case.Duals of noncommutative supersymmetric U(1) gauge theory are obtained. Duality symmetry under the interchange of fields with duals accompanied by the replacement of the noncommutativity parameter \Theta_{\mu\nu} with \tilde{\Theta}_{\mu \nu} = \epsilon_{\mu\nu\rho\sigma}\Theta^{\rho\sigma} of the non--supersymmetric case is broken at the level of actions. We proposed a noncommutative parent action for the component fields which generates actions possessing this duality symmetry.Comment: Typos corrected. Version which will appear in JHE