N=4 Topological Amplitudes and String Effective Action

Abstract

Certain scattering amplitudes in the gravitational sector of type II string theory on K3 x T^2 are found to be computed by correlation functions of the N=4 topological string. This analysis extends the already known results for K3 by Berkovits and Vafa, which correspond to six-dimensional terms in the effective action, involving four Riemann tensors and 4g-4 graviphotons, R^4T^{4g-4}, at genus g. We find two additional classes of topological amplitudes that use the full internal SCFT of K3 x T^2. One of these string amplitudes is mapped to a 1-loop contribution in the heterotic theory, and is studied explicitly. It corresponds to the four-dimensional term R^2(ddΦ)^2T^{2g-4}, with Φa Kaluza-Klein graviscalar from T^2. Finally, the generalization of the harmonicity relation for its moduli dependent coupling coefficient is obtained and shown to contain an anomaly, generalizing the holomorphic anomaly of the N=2 topological partition function F_g.

61 pages, 3 figures

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• Topological Amplitudes and Physical Couplings in String Theory
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Borcherds Algebras and N=4 Topological Amplitudes
• Supersymmetry Constraints and String Theory on K3
• A New Class of N=2 Topological Amplitudes
• Probing the Moduli Dependence of Refined Topological Amplitudes
• Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation
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• N=4 BPS black holes and octonionic twistors
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• N=4 Topological Amplitudes and Black Hole Entropy