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

TL;DR

This paper demonstrates that Morita equivalence relates abelian noncommutative field theories to nonabelian twisted theories on ordinary space, specifically showing this for a conformal field theory obtained via m-reduction, with applications to quantum Hall systems.

Contribution

It establishes the Morita equivalence for a specific conformal field theory obtained through m-reduction, extending the understanding of noncommutative field theories.

Findings

Morita equivalence holds for the m-reduction conformal field theory.

Equivalence between abelian noncommutative and nonabelian twisted theories.

Application to quantum Hall fluid at Jain fillings.

Abstract

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.