Notes on extended conformal algebras

Integer spin primary fields and their operator algebras with Energy-Momentum tensor in two dimensional bosonic conformal field theories (Feigin-Fuchs construction) are studied. A general method for calculating integer spin primary fields is given. It is shown that the generalization of the spin-3 algebra of Fateev and Zamolodchikov does not exist when the number of participating boson fields is greater than four. In a similar way higher spin (s ≥ 4) algebras are shown to be incompatible with a requirement of solvability. (author)