SUPERSYMMETRIC GAUGE-THEORIES IN 5-DIMENSIONS AND 6-DIMENSIONS

We investigate consistency conditions for supersymmetric gauge theorie s in higher dimensions. First, we give a survey of Seiberg's necessary conditions for the existence of such theories with simple groups in f ive and six dimensions. We then make some comments on how theories in different dimensions are related. In particular, we discuss how the La ndau pole can be avoided in theories that are not asymptotically free in four dimensions, and the mixing of tensor and vector multiplets in dimensional reduction from six dimensions. (C) 1997 Elsevier Science B .V.