Finiteness in SU(3) 3 models

We consider N = 1 supersymmetric gauge theories based on the group SU ( N ) 1 × SU ( N ) 2 × … × SU ( N ) k with matter content ( N , N * , 1, …, 1) + (1, N , N * , …, 1) + … + ( N * , 1, 1, …, N), which are finite if and only if there are exactly three generations. We study in particular two models with SU (3) 3 as gauge group, an all‐loop and a two‐loop finite model, and we examine their predictions concerning the third generation quark masses.