Higher-Order Gravitational Couplings and Modular Forms in $N=2,D=4$ Heterotic String Compactifications

Physics – High Energy Physics – High Energy Physics - Theory

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39 pages, Latex

Scientific paper

10.1016/S0550-3213(96)90141-8

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-II description, this equation coincides with the holomorphic anomaly equation for type-II compactifications in the limit that a specific K\"ahler-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.

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