BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form

Understand

We study BPS saturated one-loop amplitudes in type II string theory compactified on K3 x T^2.

• The classes of amplitudes we consider are only sensitive to the very basic topological data of the internal K3 manifold.
• As a consequence, the integrands of the former are related to the elliptic genus of K3, which can be decomposed into representations of the internal N=4 superconformal algebra.
• Depending on the precise choice of external states these amplitudes capture either only the contribution of the short multiplets or the full series including intermediate multiplets.