Open superstrings à la Polyakov

We set up the Polyakov path integral formalism for the type-I superstring at tree and one-loop level of string perturbation theory. The relevant super-Teichmüller parameters, conformal Killing spinors, and functional determinants are given explicitly. As an application the one-loop vacuum energy for the open superstring is computed and shown to vanish for the torus, Klein bottle, cylinder and Möbius strip separately.