One loop renormalizability of supersymmetric Yang-Mills theories on noncommutative two-torus

We argue that Yang-Mills theory on noncommutative torus, expressed in the F ourier modes, is described by a gauge theory in a usual commutative space, the gauge group being a generalization of the area preserving diffeomorphis ms to the noncommutative case. In this way, performing the loop calculation s in this gauge theory in the continuum limit, we show that this theory is one loop renormalizable, and discuss the UV and IR limits. The moduli space of the vacua of the noncommutative super Yang-Mills theories in 2+1 dimens ions is discussed.