Perturbative Couplings and Modular Forms in N=2 String Models with a Wilson Line

Abstract

We consider a class of four parameter D=4, N=2 string models, namely heterotic strings compactified on K3 times T2 together with their dual type II partners on Calabi-Yau three-folds. With the help of generalized modular forms (such as Siegel and Jacobi forms), we compute the perturbative prepotential and the perturbative Wilsonian gravitational coupling F1 for each of the models in this class. We check heterotic/type II duality for one of the models by relating the modular forms in the heterotic description to the known instanton numbers in the type II description. We comment on the relation of our results to recent proposals for closely related models.

42 pages, LaTeX, revised version contains additional references

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• (0,2) Heterotic Gauge Couplings and their M-Theory Origin
• Equivalence of Geometric Engineering and Hanany-Witten via Fractional Branes
• Exact Gravitational Threshold Correction in the FHSV Model
• Exponentially Large Extra Dimensions
• A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces
• Physics of Infinite Complex Structure Limits in eight Dimensions
• Generalised universality of gauge thresholds in heterotic vacua with and without supersymmetry
• Mathieu Moonshine and N=2 String Compactifications
• String Vacua with N=2 Supersymmetry in Four Dimensions
• D-instanton and polyinstanton effects from type I' D0-brane loops
• The effect of Wilson line moduli on CP-violation by soft supersymmetry breaking terms
• Topological Amplitudes in Heterotic Strings with Wilson Lines
• Probing the Moduli Dependence of Refined Topological Amplitudes
• Heterotic string on the CHL orbifold of K3
• Borcherds Algebras and N=4 Topological Amplitudes
• Topics in Cubic Special Geometry
• Analytic Periods via Twisted Symmetric Squares
• $\mathcal{N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
• Witten Anomaly in 4d Heterotic Compactificaitons with N = 2 Supersymmetry
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• Jacobi Forms of Higher Index and Paramodular Groups in N=2, D=4 Compactifications of String Theory
• On Mathieu moonshine and Gromov-Witten invariants
• Flat-brane Compactifications in Supergravity Induced by Scalars
• The Master Equation for the Prepotential-Pub
• N=1 Dual String Pairs and their Modular Superpotentials
• Systematics of string loop threshold corrections in orbifold models
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines
• Direct Computation of Monodromy Matrices and Classification of 4d N=2 Heterotic--IIA Dual Vacua