North-Holland BRST l QUANTIZATION OF THE GREEN-SCHWARZ SUPERSTRING

We apply a one-step Noether extended BRST procedure (BRST 1 procedure) toquantize 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 BRST 1 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) BRST 1 symmetry of the theory in the recently discovered covariant gauge where the action is quadratic in fields. We find that the BRST ~ 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 BRST ~ 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 BRST l symmetry are satisfied. We give examples ofother systems with infinite variables where this is not the case. 1