Green-Schwarz superstring theory in two dimensions and topological field theories

It is shown that the algebra associated with the local κ-supersymmetry in the Green-Schwarz superstring theory in d =2 dimensions closes off shell. We quantize the theory in a Lorentz covariant fashion by using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky, and derive a quantum mechanically consistent, gauge-fixed theory, which can be interpreted as a κ-supersymmetric extension of conformal topological gravity.