The origin of Calabi-Yau crystals in BPS states counting

The origin of Calabi-Yau crystals in BPS states counting

Blog Article

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 On-board Multi-User Detection Algorithm Based on Conditional Neural Process 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 Antiangiogenic agents targeting different angiogenic pathways have opposite effects on tumor hypoxia in R-18 human melanoma xenografts Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories.