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Elliptic genera from multi-centers. (English) Zbl 1388.83800

Summary: I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multicenter configurations. I present a simple procedure that allows for the enumeration of all multi-center configurations contributing to the polar sector of the elliptic genera – explicitly verifying this in the cases of the quintic in \(\mathbb P^4\), the sextic in \(\mathbb{WP}_{(2,1,1,1,1)}\), the octic in \(\mathbb{WP}_{(4,1,1,1,1)}\) and the dectic in \(\mathbb{WP}_{(5,2,1,1,1)}\). With an input of the corresponding ‘single-center’ indices (Donaldson-Thomas invariants), the polar terms have been known to determine the elliptic genera completely. I argue that this multi-center approach to the low-lying spectrum of the elliptic genera is a stepping stone towards an understanding of the exact microscopic states that contribute to supersymmetric single center black hole entropy in \(\mathcal N=2\) supergravity.

MSC:

83E50 Supergravity
83C57 Black holes
83E30 String and superstring theories in gravitational theory

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