Elliptic genera from multi-centers

Abstract

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 multi-center 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\textemdash 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.

arXiv comment30+1 pages, Published Version

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Cited by in corpus (2)

• The full space of BPS multicenter states with pure D-brane charges
• BPS Dendroscopy on Local $P^2$