CONTINUING BETWEEN CLOSED AND OPEN STRINGS

A family of dual models is defined that interpolates between the tree diagrams of non-orientable bosonic closed-string theory (which has a massless spin-2 state) and the open-string theory with no internal symmetry (in which the lowest-mass spin-2 state is massive). These models are parametrized by the intercept, DELTA, of the leading Regge pole. The only models that have an infinite-dimensional conformal invariance and are consequently free of ghosts are the two familiar string theories with DELTA = 2 (closed strings) and DELTA = 1 (open strings with no internal symmetry). For arbitrary DELTA the models are invariant under the finite dimensional conformal group, SO(DELTA, 2), which guarantees the crossing symmetry and consistent factorization of tree amplitudes. The spectrum of the level-two states is exhibited explicitly as DELTA-varies from 2 to 1 in order to illustrate the manner in which the graviton (the lowest-mass spin-2 state) acquires a mass. The scalar ghost generically associated with massive gravity cancels with the "dilaton" precisely at DELTA = 1.