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Topological defects (vortices) of the b field, if present in the bulk, change the relation between fields bμi and Aμ. Note, however, that these defects cost a large energy (see also the discussion in Appendix). Therefore, we do not consider them.
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It is important that at the edge ∂μ jiμ ≠0, therefore the charge density is not determined by the b field. In other words the edge deformation does not generate the topological reconstruction in the bulk and leads only to the accumulation of the charge.
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Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge
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