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We study the Morita equivalence for field theories on noncommutativetwo-tori. For rational values of the noncommutativity parameter $\theta $ (inappropriate units) we show the equivalence between an abelian noncommutativefield theory and a nonabelian theory of twisted fields on ordinary space. Weconcentrate on a particular conformal field theory (CFT), the one obtained bymeans of the m-reduction procedure (V. Marotta, J. Phys. A 26 (1993) 3481; Mod.Phys. Lett. A 13 (1998) 853; Nucl. Phys. B 527 (1998) 717), and show that theMorita equivalence also holds at this level. An application to the physics of aquantum Hall fluid at Jain fillings \nu =m/2pm+1 is explicitly considered inorder to further elucidate such a correspondence.

The m-reduction in Conformal Field Theory as the Morita equivalence on two-tori