A.V.Bratchikov ∗ Kuban State Technological University,

Generalized abelian coset conformal field theories. Abstract Primary fields and correlation functions of an arbitrary abelian coset conformal field theory are explicitly expressed in terms of the associated W algebra and u(1) d currents.The coset theory has global abelian symmetry. In this paper we study conformal field theories based on the generalized coset construction [1-3] K(m) = L(m) − L u (m), m ∈ Z, (1) where L(m) , L u (m) are Virasoro generators and L u (m) are quadratic in affinê u(1) d currents which have unit conformal dimensions with respect to L(m) and L u (m). (For a review see [4]). When L(m) are given by Sugawara construction for the affine Lie algebrâ g we have g/u(1) d coset constructions. The su(2)/u(1) coset conformal field theory is equivalent to the Z k invariant parafermion theory whose studies were initiated by Fateev and Zamolodchikov [5]. For an arbitrary simple Lie algebra g the g/u(1) d models were studied in refs. [6-9].