All-order Finiteness in N = 1 SYM Theories: Criteria and Applications

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