ALL-ORDER FINITENESS IN N=1 SYM THEORIES - CRITERIA AND APPLICATIONS

As a motivation, we first recall the possible connection of electric-m agnetic duality to finiteness in N=1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishi ng of the beta-functions at all orders) in N = 1 SYM. Finally, we appl y this finiteness criterion to an SU(5) SGUT. The latter turns out to be all-order finite if one imposes additional symmetries.