Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

Abstract

The restrictions of target-space duality are imposed at the perturbative level on the holomorphic Wilsonian couplings that encode certain higher-order gravitational interactions in N = 2, D = 4 heterotic string compactifications. A crucial role is played by non-holomorphic corrections. The requirement of symplectic covariance and an associated symplectic anomaly equation play an important role in determining their form. For models which also admit a type-11 description, this equation coincides with the holomorphic anomaly equation for type-II compactifications in the limit that a specific Kähler-class modulus grows large. We explicitly evaluate some of the higher-order couplings for a toroidal compactification with two moduli T and U, and we express them in terms of modular forms.