We consider the maximal supersymmetric pure Yang-Mills theories on six and eight dimensional space. We determine, in a systematic way, all the possible fractions of supersymmetry preserved by the BPS states and present the corresponding “self-dual” BPS equations. In six dimensions the intrinsic one has 1/4 supersymmetry, while in eight dimensions, 1/16, $2/16,\dots ,6/16.$ We apply our results to some explicit BPS configurations of finite or infinite energy on commutative or noncommutative spaces.

• Received 6 May 2002

DOI:https://doi.org/10.1103/PhysRevD.66.025021