Convergent Yang-Mills Matrix Theories

Abstract

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 $D\ge D_c$, 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.

21 pages, no figures, JHEP style, typos corrected, 1 reference added

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