N=4 super Yang-Mills matrix integrals for almost all simple gauge groups -: art. no. 012

In this paper the partition function of N = 4 D = 0 super Yang-Mills matrix theory with arbitrary simple gauge group is discussed. We explicitly computed its value for all classical groups of rank r less than or equal to 11 and for the exceptional groups G(2), F-4 and E-6. In the case of classical groups of arbitrary rank we conjecture general formulas for the B-r, C-r and D-r series in addition to the known result for the A r series. Also, the relevant boundary term contributing to the Witten index of the corresponding supersymmetric quantum mechanics has been explicitly computed as a simple function of rank for the orthogonal and symplectic groups SO(2N + 1), Sp(2N), SO(2N).