Finite Yang-Mills Integrals

We use Monte Carlo methods to directly evaluate D-dimensional SU(N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for D = 3, N ≥ 4 and D = 4, N ≥ 3 and, lastly, D ≥ 5, N ≥ 2. We conclude that the D = 3 and D = 4 integrals exist in the large N limit, and therefore lead to a well-defined, new type of Eguchi-Kawai reduced gauge theory. For the supersymmetric case, we check, up to SU(5), recently proposed exact formulas for the D = 4 and D = 6 D-instanton integrals, including the explicit form of the normalization factor needed to interpret the integrals as the bulk contribution to the Witten index. ∗[email protected] †[email protected] ‡Supported in part by EU Contract FMRX-CT96-0012