A Monoidal Category for Perturbed Defects in Conformal Field Theory

Starting from an abelian rigid braided monoidal category C we define an abelian rigid monoidal category CF which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational vertex operator algebra we consider the charge-conjugation CFT constructed form V (the Cardy case). Then C = Rep(V ) and an object in CF corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in CF an operator on the space of states of the CFT, the perturbed defect operator, and show that the assignment factors through the Grothendieck ring of CF . This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT. Email: [email protected] Email: [email protected]