Twisted Conformal Field Theories and Morita equivalence

TL;DR

This paper explores the Morita equivalence between noncommutative and ordinary conformal field theories, focusing on a specific m-reduction CFT and its implications for quantum Hall systems, revealing a novel relationship in strongly correlated physics.

Contribution

It demonstrates that a particular m-reduction conformal field theory is Morita equivalent to a noncommutative field theory, linking noncommutativity with conformal field theory structures and quantum Hall physics.

Findings

Establishes isomorphism between abelian NCFT and twisted field theories on ordinary space.

Shows m-reduction procedure as the image of Morita duality in ordinary space.

Applies the framework to quantum Hall fluids at Jain fillings, clarifying the role of noncommutativity.

Abstract

The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter theta (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a non-abelian 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 (V. Marotta, J. Phys. A 26 (1993) 3481; V. Marotta, Mod. Phys. Lett. A 13} (1998) 853; V. Marotta, Nucl. Phys. B 527 (1998) 717; V. Marotta, A. Sciarrino, Mod. Phys. Lett. A 13 (1998) 2863), 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 nu =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 (A. P. Polychronakos, arXiv:0706.1095v2).