ESI The Erwin Schr odinger

Chiral orbifold models are deened as gauge eld theories with a nite gauge group ?. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative deenite integral invariant bilinear form on its Lie algebra. Any nite group ? of inner automorphisms or A (in particular, any nite subgroup of G) gives rise to a gauge theory with a chiral subalgebra A ? A of local observables invariant under ?. A set of positive energy A ? modules is constructed whose characters span, under some assumptions on ?, a nite dimensional unitary representation of SL(2; Z). We compute their asymptotic dimensions (thus singling out the nontrivial orbifold modules) and nd explicit formulae for the modular transformations and hence, for the fusion rules. As an application we construct a family of rational conformal eld theory (RCFT) extensions of W 1+1 that appear to provide a bridge between two approaches to the quantum Hall eeect.