A simple physical interpretation of the critical dimension of space- time in dual models

The energy due to zero point fluctuations of the dual string is calculated and shown to be divergent. It is made finite by introducing a cut-off. The result is non-covariant but invariant under reparametrization, so one has to modify the classical Lagrangian so as to get a covariant result. It is then shown that this leads to the well-known relation relating the mass squared of the lowest state to the number of dimensions of space-time. This result is independent of the cut-off and shows clearly the physical significance of the critical dimensions of space-time. Similar considerations for the Neveu-Schwarz model are also discussed. (6 refs).