Zamolodchikov metric and effective Lagrangians in string theory

Using the (1,0) superspace formalism, we calculate the Zamolodchikov metrics for moduli and 27, $\overline{27}$ matter scalars in the untwisted sector of (2,2)-symmetric $Z_N$ orbifolds. These metrics are found to be the same as the metrics in the effective Lagrangians of untwisted moduli and matter scalars obtained previously by different methods. This result is strong evidence that the Zamolodchikov metric and the metric on the manifold of scalars in the effective Lagrangian are identical for all string theories.