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We prove that SU(N) bosonic Yang-Mills matrix integrals are convergent for dimension (number of matrices) $Dge D_c$. It is already known that $D_c=5$ for N=2; we prove that $D_c=4$ for N=3 and that $D_c=3$ for $Nge 4$. These results are consistent with the numerical evaluations of the integrals by Krauth and Staudacher.
We summarize recent progress in lattice studies of four-dimensional N=4 supersymmetric Yang--Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry a
We give a comparison of the spectrum of Yang-Mills theory in $D=3+1$, recently derived with a strong coupling expansion, with lattice data. We verify excellent agreement also for 2$^{++}$ glueball. A deep analogy with the $D=2+1$ case is obtained and
We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU($N$) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and t
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well wi
In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanzigers horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evalu