  We consider the conformally-invariant coupling of topologically massive
gravity to a dynamical massless scalar field theory on a three-manifold with
boundary. We show that, in the phase of spontaneously broken Lorentz and Weyl
symmetries, this theory induces the target space zero mode of the vertex
operator for the string dilaton field on the boundary of the three-dimensional
manifold. By a further coupling to topologically massive gauge fields in the
bulk, we demonstrate directly from the three-dimensional theory that this
dilaton field transforms in the expected way under duality transformations so
as to preserve the mass gaps in the spectra of the gauge and gravitational
sectors of the quantum field theory. We show that this implies an intimate
dynamical relationship between T-duality and S-duality transformations of the
quantum string theory. The dilaton in this model couples bulk and worldsheet
degrees of freedom to each other and generates a dynamical string coupling.
