Gauge field theory of covariant strings

We present a gauge covariant second-quantized field theory of strings which is explicitly invariant under the gauge transformations generated by the Virasoro algebra. Unlike the old field theory strings this new formulation is Lorentz covariant as well as gauge covariant under the continuous group Diff(S1) and its central extension. We derive the free action: L=PHI(X)+[idsub(tau)-(L0-1)]PPHI(X), in the same way that Feynman derived the Schroedinger equation from the path integral formalism. The action is manifestly invariant under the gauge transformation deltaPHI(X)=Σsup(proportional)sub(n=1)epsilonsub(-n)Lsub(-n)PHI(X), where P is a projection operator which annihilates spurious states. We give three distinct formulations of this operator P to all orders, the first based on extracting the operator from the functional formulation of the Nambu-Goto action, and the second and third baded on inverting the Shapovalov matrix on a Verma module. This gauge covariant formulation can be easily extended to the Green-Schwarz superstring. One elegant application of these methods is to re-express the old Neveu-Schwarz-Ramond model as a field theory which is manifestly invariant under space-time supersymmetric transformations. (orig.)