BRST1 quantization of the Green-Schwarz superstring

We apply a one-step Noether extended BRST procedure (BRST1 procedure) to quantize the Green-Schwarz heterotic string. The gauge fixed action is presented in a wide class of gauges including the unitary light-cone gauge as well as Lorentz-covariant gauges containing an infinite number of ghosts. We show that the BRST1 transformation rules and the proof of the gauge independence of the theory are simple for a particular choice of variables. We present the explicit (on-shell closed) BRST1 symmetry of the theory in the recently discovered covariant gauge where the action is quadratic in fields. We find that the BRST1 transformations of the right- and left-moving modes are separately off-shell nilpotent. We furthermore point out that in order to show that the gauge fixed action is BRST1 invariant it is necessary to regularize certain infinite summations over the fields of the theory. This regularization leads to non-trivial integrability conditions which in the case of the BRST1 symmetry are satisfied. We give examples of other systems with infinite variables where this is not the case.