Paired quantum Hall states on noncommutative two-tori

TL;DR

This paper establishes a correspondence between noncommutative field theories and ordinary space theories for quantum Hall states, revealing how noncommutativity influences the physics of quantum Hall bilayers and extending previous models.

Contribution

It demonstrates a Morita equivalence between noncommutative conformal field theories and twisted field theories for paired quantum Hall states, extending prior work on Jain series.

Findings

Morita equivalence links NCFT and twisted field theories for quantum Hall states.

Explicit analysis of the m=2 case highlights noncommutativity's role in bilayer systems.

Provides a new low-energy effective description for certain condensed matter phenomena.

Abstract

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter theta (in appropriate units), a one-to-one correspondence between an abelian noncommutative field theory (NCFT) and a non-abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings nu =m/pm+2, recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in a previous work (V. Marotta, A. Naddeo, Nucl. Phys. B 810(2009) 575) for the Jain series nu =m/2pm+1. The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.