Models in the Hierarchical Quantum Hall Effect

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 Û(1)× ̂ SU(m)1 and the W1+∞ 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 ≤ 3. 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 Û(1)× ̂ SU(m)1 representations into those of the c = m W1+∞ minimal models. Furthermore, we find the Hamiltonian whose renormalization group flow interpolates between the two models, having the W1+∞ minimal models as infra-red fixed point.