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arXiv · 1712.01985

Higher genus Siegel forms and multi-center black holes in N=4 supersymmetric string theory

Frederik Denef·Shamit Kachru·Zimo Sun·Arnav Tripathy
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Abstract

We conjecture that the Fourier coefficients of a degree three Siegel form, $1/\sqrt{\chi_{18}}$, count the degeneracy of three-center BPS bound states in type II string theory compactified on $K3 \times T^2$. We provide evidence for our conjecture in the form of consistency with physical considerations of wall-crossing, holographic bounds, and the appearance of suitable counting functions (involving the inverse of the modular discriminant $\Delta$ and the inverse of the Igusa cusp form $\Phi_{10}$) in limits where the count degenerates to involve single-center or two-center objects.

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Frederik Denef, Shamit Kachru, Zimo Sun, Arnav Tripathy. 2017-12-06. Higher genus Siegel forms and multi-center black holes in N=4 supersymmetric string theory. https://arxiv.org/abs/1712.01985

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