ar X iv : h ep - t h / 96 12 07 8 v 2 1 5 D ec 1 99 6 AFFINE ORBIFOLDS AND RATIONAL CONFORMAL FIELD

Chiral orbifold models are defined as gauge field theories with a finite gauge group Γ. 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 Γ of inner automorphisms or A (in particular, any finite subgroup of G) gives rise to a gauge theory with a chiral subalgebra A ⊂ A of local observables invariant under Γ. A set of positive energy A modules is constructed whose characters span, under some assumptions on Γ, a finite dimensional unitary representation of SL(2, Z). 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 W1+∞ that appear to provide a bridge between two approaches to the quantum Hall effect.