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arXiv · hep-th/9607184

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

Bernard de Wit·Gabriel Lopes Cardoso·Dieter Lüst·Thomas Mohaupt·Soo-Jong Rey
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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-II 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.

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Bernard de Wit, Gabriel Lopes Cardoso, Dieter Lüst, Thomas Mohaupt, Soo-Jong Rey. 1996-07-23. Higher-Order Gravitational Couplings and Modular Forms in $N=2,D=4$ Heterotic String Compactifications. https://doi.org/10.1016/s0550-3213(96)90141-8

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