  All unitary Rational Conformal Field Theories (RCFT) are conjectured to be
related to unitary coset Conformal Field Theories, i.e., gauged
Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use
subfactor theory and ideas of algebraic quantum field theory to approach coset
Conformal Field Theories. Two conjectures are formulated and their consequences
are discussed. Some results are presented which prove the conjectures in
special cases. In particular, one of the results states that a class of
representations of coset $W_N$ ($N\geq 3$) algebras with critical parameters
are irreducible, and under the natural compositions (Connes' fusion), they
generate a finite dimensional fusion ring whose structure constants are
completely determined, thus proving a long-standing conjecture about the
representations of these algebras.
