N=4 Topological Amplitudes and String Effective Action

Details N=4 Topological Amplitudes and String Effective Action N=4 Topological Amplitudes and String Effective Action

2006-10-24

arxiv.org/abs/hep-th/0610258v1

Nucl.Phys.B771:40-92,2007

Physics

High Energy Physics

High Energy Physics - Theory

61 pages, 3 figures

Scientific paper

10.1016/j.nuclphysb.2007.02.011

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(dd\Phi)^2T^{2g-4}, with \Phi a 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.

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