The non-chiral fusion rules in rational conformal field theories

We introduce a general method in order to construct the non-chiral fusion rules which determine the operator content of the operator product algebra for rational conformal field theories. We are particularly interested in the models of the complementary D−like solutions of the modular invariant partition functions with cyclic center ZN . We find that the non-chiral fusion rules have a ZN−grading structure. One of the most important requirements in the construction of two-dimensional conformal field theories (CFT), the bootstrap requirement, is the existence of a closed associative operator product algebra (OPA) among all fields [1]. The information about the OPA structure is collected in the structure constants, the computation of which is fundamental since it permits in principle the determination of all correlation functions. But unfortunately, in practice, the structure of the OPA seems to be very complicated and so is, indeed, the computation of the structure constants. The structure of the OPA is expressed by the so-called fusion rules [2], which describe how the chiral-sectors ‘vertices’, representing the holomorphic (z) and antiholomorphic ∗e-mail: [email protected]