Convergent Yang-Mills matrix theories

We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when D = 4, 6 and 10, and that correlation functions of degree k < k(c) = 2(D - 3) are convergent independently of the group. In the bosonic case we show that the partition function is convergent when D <greater than or equal to> D-c, and that correlation functions of degree k < k(c) are convergent, and calculate D-c and k(c) for each group, thus extending our previous results for SU(N). As a special case these results establish that the partition function and a set of correlation functions in the IKKT IIB string matrix model are convergent.