N=4 Topological Amplitudes and String Effective Action

TL;DR

This paper explores new topological string amplitudes in type II string theory on K3 x T^2, revealing their computation via correlation functions and their relation to heterotic string theory, extending known results and uncovering anomalies.

Contribution

It introduces two new classes of topological amplitudes involving the full internal SCFT of K3 x T^2 and generalizes the harmonicity relation with an anomaly.

Findings

Identified new topological amplitudes involving K3 x T^2

Mapped one amplitude to a 1-loop heterotic contribution

Generalized the harmonicity relation with an anomaly

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(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.