INTERNAL STRING AND GAUGE-THEORY OF THE VIRASORO GROUP

We show that any 5-dimensional field theory defined on the fibre bundle space made of a 4-dimensional space-time and the internal string S1 which is invariant under the space-time-dependent reparametrization of the string can be interpreted as a 4-dimensional gauge theory of the Virasoro group. Then, we derive the effective Lagrangian by dimensional reduction of the 5-dimensional Einstein-Yang-Mills theory, which is a gauge theory of the Virasoro-Kac-Moody group associated with P x G where P is the Poincare group and G is the grand unification group. We show that, after the inevitable symmetry breaking, the massive modes consist of the infinite tower of the spin-two multiplets corresponding to the Kac-Moody extension of P and the infinite tower of the spin-one multiplets corresponding to the Kac-Moody extension of G.