Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-02-02
Int.J.Mod.Phys. A15 (2000) 915
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX with Tcilatex Macro (included), 16 pages, no figures
Scientific paper
10.1142/S0217751X00000458
Two classes of Conformal Field Theories have been proposed to describe the Hierarchical Quantum Hall Effect:the multi-component bosonic theory, characterized by the symmetry U(1)xSU(m)_1 and the W_{1+\infty} minimal models with central charge c=m. In spite of having the same spectrum of edge excitations, they manifest differences in the degeneracy of the states and in the quantum statistics, which call for a more detailed comparison between them. Here, we describe their detailed relation for the general case, c=m and extend the methods previously published for c < 4. Specifically, we obtain the reduction in the number of degrees of freedom from the multi-component Abelian theory to the minimal models by decomposing the characters of the U(1)xSU(m)_1 representations into those of the c=m W_{1+\infty} minimal models. Furthermore, we find the Hamiltonian whose renormalization group flow interpolates between the two models, having the W_{1+\infty} minimal models as infra-red fixed point.
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