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We argue that Yang-Mills theory on noncommutative torus, expressed in the
Fourrier modes, is described by a gauge theory in a usual commutative
space, the gauge group being a generalization of the area preserving
diffeomorphisms to the noncommutative case. In this way, performing the loop
calculations in this gauge theory in the continuum limit, we show that this
theory is {\it 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 dimensions is discussed.
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