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

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

2008-10-27

arxiv.org/abs/0810.4759v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 1 figure

Scientific paper

10.1088/1126-6708/2008/08/029

We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $\theta $ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and a nonabelian theory of twisted fields on ordinary space. We concentrate on a particular conformal field theory (CFT), the one obtained by means 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 the Morita equivalence also holds at this level. An application to the physics of a quantum Hall fluid at Jain fillings \nu =m/2pm+1 is explicitly considered in order to further elucidate such a correspondence.

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