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Chiral orbifold models are defined as gauge field theories with a finitegauge group $\Gamma$. We start with a conformal current algebra A associatedwith a connected compact Lie group G and a negative definite integral invariantbilinear form on its Lie algebra. Any finite group $\Gamma$ of innerautomorphisms or A (in particular, any finite subgroup of G) gives rise to agauge theory with a chiral subalgebra $A^{\Gamma}\subset A$ of localobservables invariant under $\Gamma$. A set of positive energy $A^{\Gamma}$modules is constructed whose characters span, under some assumptions on$\Gamma$, a finite dimensional unitary representation of $SL(2,Z)$. We computetheir asymptotic dimensions (thus singling out the nontrivial orbifold modules)and find explicit formulae for the modular transformations and hence, for thefusion rules.  As an application we construct a family of rational conformal field theory(RCFT) extensions of $W_{1+\infty}$ that appear to provide a bridge between twoapproaches to the quantum Hall effect.Comment: 64 pages, amste

Affine Orbifolds and Rational Conformal Field Theory Extensions of W 1+∞