2002/08/20 by Aziz El Rhalami, El Hassan Saidi
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum many-body systems #hep-th
paper · pdf · doi:10.1088/1126-6708/2002/10/039
54 pages 11 figures, LaTex
arxiv created 2002/08/20 · openalex publication_date 2002/10/16 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We develop an effective field model for describing FQH states with rational filling factors that are not of Laughlin type. These kinds of systems, which concern single layer hierarchical states and multilayer ones, were observed experimentally; but have not yet a satisfactory non commutative effective field description like in the case of Susskind model. Using D brane analysis and fiber bundle techniques, we first classify such states in terms of representations characterized, amongst others, by the filling factor of the layers; but also by proper subgroups of the underlying U(n) gauge symmetry. Multilayer states in the lowest Landau level are interpreted in terms of systems of D2 branes; but hierarchical ones are realized as Fiber bundles on D2 which we construct explicitly. In this picture, Jain and Haldane series are recovered as special cases and have a remarkable interpretation in terms of Fiber bundles with specific intersection matrices. We also derive the general NC commutative effective field and matrix models for FQH states, extending Susskind theory, and give the general expression of the rational filling factors as well as their non abelian gauge symmetries.