DFF 257/10/96 hep-th/9610019 W1+∞ FIELD THEORIES FOR THE EDGE EXCITATIONS IN THE QUANTUM HALL EFFECT
نویسنده
چکیده
We briefly review these low-energy effective theories for the quantum Hall effect, with emphasis and language familiar to field theorists. Two models have been proposed for describing the most stable Hall plateaus (the Jain series): the multi-component Abelian theories and the minimal W1+∞ models. They both lead to a-priori classifications of quantum Hall universality classes. Some experiments already confirmed the basic predictions common to both effective theories, while other experiments will soon pin down their detailed properties and differences. Based on the study of partition functions, we show that the Abelian theories are rational conformal field theories while the minimal W1+∞ models are not.
منابع مشابه
A Unified Conformal Field Theory Description of Paired Quantum Hall States
The wave functions of the Haldane-Rezayi paired Hall state have been previously described by a non-unitary conformal field theory with central charge c = −2. Moreover, a relation with the c = 1 unitary Weyl fermion has been suggested. We construct the complete unitary theory and show that it consistently describes the edge excitations of the Haldane-Rezayi state. Actually, we show that the unit...
متن کاملStable Hierarchical Quantum Hall Fluids as W1+∞ Minimal Models
In this paper, we pursue our analysis of the W1+∞ symmetry of the lowenergy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1 + 1)-dimensional effective field theories, which are built by representations of the W1+∞ algebra. Generic W1+∞ theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular cla...
متن کاملClassification of Quantum Hall Universality Classes by W 1 + ∞ symmetry
We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as W1+∞ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul representation theory of the W1+∞ algebra leads then to a purely algebraic complete classification of hierarchical quantum Hall states, which encompasses all measured fractions. Sp...
متن کاملSUSY QuantumHall Effect on Non-Anti-Commutative Geometry
We review the recent developments of the SUSY quantum Hall effect [hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007, arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effects on supermanifolds. On each of supersphere and superplane, we investigate SUSY Landau problem and explicitly construct SUSY extensions of the Laughlin wavefunction and topological excitatio...
متن کاملModular Invariant Partition Functions in the Quantum Hall Effect
We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable...
متن کامل