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

Abstract

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. 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 chi_{10} of Sp(4,Z). We speculate on possible algebraic implications of our result on the BPS states of the N=4 type II compactification.

45 pages, LaTeX; v2: two references added, final version to appear in NPB

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Cited by in corpus (10)

• M-strings, Elliptic Genera and N=4 String Amplitudes
• Worldsheet Realization of the Refined Topological String
• Non-Abelian Tensor Towers and (2,0) Superconformal Theories
• Mock Modular Mathieu Moonshine Modules
• Heterotic string on the CHL orbifold of K3
• Mathieu moonshine in four dimensional $\mathcal{N}=1$ theories
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Mathieu Moonshine and Orbifold K3s
• One-loop Chern-Simons terms in five dimensions