Open and unoriented strings à la Polyakov

We set up the Polyakov path integral formalism for the open and unoriented bosonic string at tree and one-loop level of string perturbation theory. The relevant Teichmüller parameters, conformal Killing vectors, “large” diffeomorphisms, and functional determinants are given explicitly. As a toy application the one-loop vacuum energy for the open and closed sectors of the unoriented bosonic string is computed.