Bosonic string theory with dust

We study a modified bosonic string theory that has a pressureless 'dust' field on the string worldsheet. The dust is a real scalar field with unit gradient which breaks conformal invariance. Hamiltonian analysis reveals a time reparametrization constraint linear in the dust field momentum and a spatial diffeomorphism constraint. This feature provides a natural 'dust time' gauge in analogy with the parametrized particle. In this gauge we give a Fock quantization of the theory, which is complete and self-consistent in d < 26. The Hamiltonian of the theory is not a constraint; as a consequence the Hilbert space and mass spectrum are characterized by an additional parameter, and includes the usual string spectrum as a special case. The other sectors provide new particle spectra, some of which do not have tachyons. (paper)