Orbifold Duality Symmetries and Quantum Hall systems

Details Orbifold Duality Symmetries and Quantum Hall systems Orbifold Duality Symmetries and Quantum Hall systems

1998-06-03

arxiv.org/abs/cond-mat/9806051v2

Nucl.Phys. B538 (1999) 659-684

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

35 pages, latex file. Factors corrected in some equations, typos corrected, references added. Also some clarifications of vari

Scientific paper

10.1016/S0550-3213(98)00738-X

We consider the possible role that chiral orbifold conformal field theories may play in describing the edge state theories of quantum Hall systems. This is a generalization of work that already exists in the literature, where it has been shown that 1+1 chiral bosons living on a n-dimensional torus, and which couple to a U_1 gauge field, give rise to anomalous electric currents, the anomaly being related to the Hall conductivity. The well known $O(n,n;Z)$ duality group associated with such toroidal conformal field theories transforms the edge states and Hall conductivities in a way which makes interesting connections between different theories, e.g. between systems exhibiting the integer and fractional quantum Hall effect. In this paper we try to explore the extension of these constructions to the case where such bosons live on a n-dimensional orbifold. We give a general formalism for discussing the relevant quantities like the Hall conductance and their transformation under the duality groups present in orbifold compactifications. We illustrate these ideas by presenting a detailed analysis of a toy model based on the two-dimensional Z_3 orbifold. In this model we obtain new classes of filling fractions, which generally the correspond to fermionic edge states carrying fractional electric charge. We also consider the relation between orbifold edge theories and Luttinger liquids (LL's), which in the past have provided important insights into the physics of quantum Hall systems.

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