OPEN DESCENDANTS IN CONFORMAL FIELD-THEORY

Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalization s of the fusion algebra. The first is needed even in the relatively si mple case of diagonal models. It leads to a new tensor that satisfies the fusion algebra, but whose entries are signed integers. The second is needed when dealing with non-diagonal models, where Cardy's ansatz does not apply. It leads to a new tensor with positive integer entries , that satisfies a set of polynomial equations and encodes the classif ication of the allowed boundary operators.