String theory as it is usually presented mathematically is a theory of parametrized strings. A physical theory however should only involve non- parametrized strings. In other words the theory should be invariant under the diffeomorphism group of the circle. The authors show that the vacuum states in possible quantum field theories of strings give rise to certain holomorphic line bundles on the infinite dimensional manifold obtained by quotienting the diffeomorphism group by the rotations. For a sensible quantum field theory these bundles have to be flat. The curvature of the bundles is calculated and shown to depend on two independent parameters. Setting these to zero gives the famous condition that space-time should have dimension 26 and the requirement that the ghost Fermi sea level be chosen so that the vacuum is invariant under SL(2,R), considered as a subgroup of the diffeomorphisms of the circle.