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High Energy Physics - Theory
Title: The Origin of Calabi-Yau Crystals in BPS States Counting
(Submitted on 5 Jan 2024 (v1), last revised 27 Mar 2024 (this version, v3))
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.
Submission history
From: Jiakang Bao [view email][v1] Fri, 5 Jan 2024 13:08:36 GMT (2704kb,D)
[v2] Sun, 14 Jan 2024 20:41:06 GMT (2710kb,D)
[v3] Wed, 27 Mar 2024 12:08:29 GMT (2664kb,D)
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