Modular invariant partition functions in the quantum Hall effect
نویسندگان
چکیده
منابع مشابه
Modular 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...
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Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks....
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A complete classification of the WZNW modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of SU(2), and level 1 of all simple algebras. In this paper we solve the classification problem for SU(3) modular invariant partition functions. Our approach will also be applicable to other affine Lie algebras, and we include some p...
متن کاملThe Rank Four Heterotic Modular Invariant Partition Functions
In this paper, we develop several general techniques to investigate modular invariants of conformal field theories whose algebras of the holomorphic and anti-holomorphic sectors are different. As an application, we find all such “heterotic” WZNW physical invariants of (horizontal) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank ≤ 3 have b...
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The conformal spectra of the critical dilute A–D–E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A–D–E classification of unitary minimal modular invariant partition functions given by Cappelli, Itzykson and Zuber. In branches 3 and 4 the results indicate that the modular invariant partition func...
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ژورنال
عنوان ژورنال: Nuclear Physics B
سال: 1997
ISSN: 0550-3213
DOI: 10.1016/s0550-3213(97)00110-7