Towards covariantly quantized D=10 type-II Green-Schwarz σ-models

The complete gauge algebra of all symmetries which occur in D=10 Green-Schwarz formulations of closed superstring theories are investigated in the presence of nontrivial backgrounds. Explicit expressions for nonclosure functions required for the Batalin-Vilkovisky quantization technique are obtained. This technique is then employed to covariantly quantize the σ-model describing type II-A Green-Schwarz superstrings propagating in N=2, D=10 curved superspace, using a gauge-fixing fermion analogous to the one proposed recently for the quantization of the free D=10 heterotic string. The ultraviolet properties of the one-loop d=2 effective action are examined in some detail. In particular, we show that the violation of space-time Lorentz invariance found earlier using a Lorentz noncovariant quantization ansatz disappears in this manifestly covariant formulation. (orig.)