UNIFYING W-ALGEBRAS

We show that quantum Casimir W-algebras truncate at degenerate values of the central charge c to a smaller algebra if the rank is high enoug h: Choosing a suitable parametrization of the central charge in terms of the rank of the underlying simple Lie algebra, the field content do es not change with the rank of the Casimir algebra any more. This lead s to identifications between the Casimir algebras themselves but also gives rise to new, 'unifying' W-algebras. For example, the kth unitary minimal model of WA(n) has a unifying W-algebra of type W(2,3,..., k2 + 3k + 1). These unifying W-algebras are non-freely generated on the quantum level and belong to a recently discovered class of W-algebras with infinitely, non-freely generated classical counterparts. Some of the identifications are indicated by level-rank-duality leading to a c oset realization of these unifying W-algebras. Other unifying W-algebr as are new, including e.g. algebras of type WD(-n). We point out that all unifying quantum W-algebras are finitely, but non-freely generated .