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Affine orbifolds and rational conformal field theory extensions of W_{1+infinity}
Chiral orbifold models are defined as gauge field theories with a finite
gauge group . We start with a conformal current algebra A associated
with a connected compact Lie group G and a negative definite integral invariant
bilinear form on its Lie algebra. Any finite group of inner
automorphisms or A (in particular, any finite subgroup of G) gives rise to a
gauge theory with a chiral subalgebra of local
observables invariant under . A set of positive energy
modules is constructed whose characters span, under some assumptions on
, a finite dimensional unitary representation of . We compute
their asymptotic dimensions (thus singling out the nontrivial orbifold modules)
and find explicit formulae for the modular transformations and hence, for the
fusion rules.
As an application we construct a family of rational conformal field theory
(RCFT) extensions of that appear to provide a bridge between two
approaches to the quantum Hall effect.Comment: 64 pages, amste
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