image topological amplitudes and string effective action Original Research Article

Certain scattering amplitudes in the gravitational sector of type II string theory on image are found to be computed by correlation functions of the image 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 image graviphotons, image, at genus g. We find two additional classes of topological amplitudes that use the full internal SCFT of image. 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 image, with Φ a Kaluza–Klein graviscalar from image. 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 image topological partition function image.