The elliptic genus of Calabi-Yau 3- and 4-folds, product formulae and generalized Kac-Moody algebras

Abstract

In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where K3 is replaced by a general Calabi-Yau 3- or 4-fold. In all cases there seems to be a generalized Kac-Moody algebra involved, whose denominator formula appears in the result.

10 pages, latex, no figures

References in corpus (4)

• Algebras, BPS States, and Strings
• Counting Dyons in N=4 String Theory
• Constraints on Low-Dimensional String Compactifications
• $N=2$ heterotic string threshold correction, $K3$ surface and generalized Kac-Moody superalgebra

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• A Twist in the Dyon Partition Function
• Weight One Jacobi Forms and Umbral Moonshine
• N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds
• Jacobi Forms of Higher Index and Paramodular Groups in N=2, D=4 Compactifications of String Theory