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

1996/07/23 by Bernard de Wit, Gabriel Lopes Cardoso, Dieter Lüst +2 · 29 citations
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Compactification (mathematics) #Heterotic string theory #Holomorphic function #Mathematical physics #Mathematics #Moduli space #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Symplectic geometry #Theoretical physics #hep-th

paper · pdf · doi:10.1016/s0550-3213(96)90141-8

published in Nuclear Physics B 481(1-2), 353-388 (Elsevier BV) · 39 pages, Latex

arxiv created 1996/07/23 · openalex publication_date 1996/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• Strong-weak coupling duality and non-perturbative effects in string theory
• String theory dynamics in various dimensions
• Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL (2,Z) invariance in string theory
• Evidence for F-theory
• Algebras, BPS states, and strings
• Massless black holes and conifolds in string theory
• Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
• Geometric singularities and enhanced gauge symmetries
• Moduli dependence of string loop corrections to gauge coupling constants
• STRONG–WEAK COUPLING DUALITY IN FOUR-DIMENSIONAL STRING THEORY
• Unity of superstring dualities
• K3-fibrations and heterotic-type II string duality
• Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications
• Exact results for N = 2 compactifications of heterotic strings

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• Counting higher genus curves in a Calabi-Yau manifold