A newN= 6 superconformal algebra

In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO ₆ current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The commutation relations of this algebra, which we will refer to asCK ₆, are represented by short distance operator product expansions (OPE). We constructCK ₆, as a subalgebra of theSO(6) superconformal algebra K₆, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK ₆ has no nontrivial central extensions. Partially supported by NSC grant 85-2121-M-006-019 of the ROC. Partially supported by NSF grant DMS-9622870.