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We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in thegauge coupling constant or, equivalently, in the number of ordinary gaugefields. We do so for arbitrary compact gauge groups in arbitrary unitaryrepresentations. For gauge and matter fields, we fully work out \theta-exactnon-hybrid Seiberg-Witten maps up to order three in the number of ordinarygauge fields.

Computing the \theta-exact Seiberg-Witten map for arbitrary gauge groups