AFFINE ORBIFOLDS AND RATIONAL CONFORMAL FIELD-THEORY EXTENSIONS OF W1+INFINITY

Chiral orbifold models are defined as gauge field theories with a fini te gauge group Gamma. We start with a conformal current algebra U asso ciated with a connected compact Lie group G and a negative definite in tegral invariant bilinear form on its Lie algebra. Any finite group Ga mma of inner automorphisms or U (in particular, any finite subgroup of G) gives rise to a gauge theory with a chiral subalgebra U-Gamma subs et of U of local observables invariant under Gamma. A set of positive energy U-Gamma modules is constructed whose characters span, under som e assumptions on Gamma, a finite dimensional unitary representation of SL(2, Z). We compute their asymptotic dimensions (thus singling out t he nontrivial orbifold modules) and find explicit formulae for the mod ular transformations and hence, for the fusion rules. As an applicatio n we construct a family of rational conformal field theory (RCFT) exte nsions of W1+infinity that appear to provide a bridge between two appr oaches to the quantum Hall effect.