BPS-saturated string amplitudes: K3 elliptic genus and Igusa cusp form image Original Research Article

We study BPS-saturated one-loop amplitudes in type II string theory compactified on image. 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 image 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. In the latter case we can define a generating functional for the whole class, which we show is given by the weight ten Igusa cusp form image of image. We speculate on possible algebraic implications of our result on the BPS states of the image type II compactification.