Gauge-covariant deformations, symmetries, and free parameters of string theory

We examine the first-order deformations of the stress tensor of the free bosonic conformal field theory which preserve the two mutually commuting copies of the Virasoro algebra and involve just two derivatives. We find a much richer structure than canonical deformations, and, without using ghosts, exhibit a distinct deformation of the stress tensor for every solution to the linearized covariant equations of motion for the massless modes of the bosonic string. We are thus able to derive explicitly all general coordinate and two-form gauge transformations, about flat space-time, and we argue that all zero modes generate symmetries if we admit auxiliary fields. We also show that, to first order, there exists in addition a finite number of deformations, associated with world-sheet instantons, which may correspond to free parameters of string theory