Twisted Conformal Field Theories and Morita equivalence

The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter θ (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a nonabelian theory of twisted fields on ordinary space. We focus on a particular conformal field theory (CFT), the one obtained by means of the m-reduction procedure [1], and show that it is the Morita equivalent of a NCFT. Finally, the whole m-reduction procedure is shown to be the image in the ordinary space of the Morita duality. An application to the physics of a quantum Hall fluid at Jain fillings ν = m 2pm+1 is explicitly discussed in order to further elucidate such a correspondence and to clarify its role in the physics of strongly correlated systems. A new picture emerges, which is very different from the existing relationships between noncommutativity and many body systems [2].