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arXiv · 2401.02792

The Origin of Calabi-Yau Crystals in BPS States Counting

Jiakang Bao·Rak-Kyeong Seong·Masahito Yamazaki
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Abstract

We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. For Calabi-Yau threefolds, we reproduce the crystal melting models long known in the literature. For Calabi-Yau fourfolds, however, we find that the crystal does not contain the full information for the BPS degeneracy and we need to explicitly evaluate non-trivial weights assigned to the crystal configurations. Our discussions treat Calabi-Yau threefolds and fourfolds on equal footing, and include discussions on elliptic and rational generalizations of the BPS states counting, connections to the mathematical definition of generalized Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories.

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Jiakang Bao, Rak-Kyeong Seong, Masahito Yamazaki. 2024-01-05. The Origin of Calabi-Yau Crystals in BPS States Counting. https://doi.org/10.1007/jhep03(2024)140

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