1996/05/30 by Andrea Cappelli, Guillermo R. Zemba · 84 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Conformal field theory #Conformal map #Electron #Geometry #Invariant (physics) #Mathematical physics #Mathematics #Modular design #Modular invariance #Partition function (quantum field theory) #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum, superfluid, helium dynamics #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00110-7
published in Nuclear Physics B 490(3), 595-632 (Elsevier BV) · Latex, 38 pages, 1 table (one minor error has been corrected)
arxiv created 1996/05/30 · openalex publication_date 1997/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W-infinity algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with U(1)xSU(m) affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.