On the classification of bulk and boundary conformal field theories

The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued representations of the fusion algebra. A complete solution not only yields the admissible boundary conditions but also gives valuable information on the bulk properties. (C) 1998 Published by Elsevier Science B.V. All rights reserved.