The Lie h - Invariant Conformal Field Theories and the Lie h - Invariant Graphs ∗

We use the Virasoro master equation to study the space of Lie h-invariant conformal field theories, which includes the standard rational conformal field theories as a small subspace. In a detailed example, we apply the general theory to characterize and study the Lie h-invariant graphs, which classify the Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The Lie characterization of these graphs is another aspect of the recently observed Lie group-theoretic structure of graph theory. This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY90-21139. The work of N. O. is supported in part by the Deutsche Forschungsgemeinschaft. email: [email protected],42070::HALPERN, [email protected] email: [email protected], 42070::KIRITSIS, [email protected] Address after October 1, 1991: Lab. de Physique Théorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231, Paris, CEDEX 05, FRANCE. email: 13581::OBERS, [email protected]