HIGHER-ORDER GRAVITATIONAL COUPLINGS AND MODULAR-FORMS IN N=2, D=4 HETEROTIC STRING COMPACTIFICATIONS

The restrictions of target-space duality are imposed at the perturbati ve level on the holomorphic Wilsonian couplings that encode certain hi gher-order gravitational interactions in N = 2, D = 4 heterotic string compactifications, A crucial role is played by non-holomorphic correc tions. The requirement of symplectic covariance and an associated symp lectic anomaly equation play an important role in determining their fo rm. For models which also admit a type-II description, this equation c oincides with the holomorphic anomaly equation for type-II compactific ations in the limit that a specific Kahler-class modulus grows large. We explicitly evaluate some of the higher-order couplings for a toroid al compactification with two moduli T and U, and we express them in te rms of modular forms.