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4d Crystal Melting, Toric Calabi-Yau 4-Folds and Brane Brick Models
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abstract
We introduce a class of 4-dimensional crystal melting models that count the BPS bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by the brane brick model associated to the Calabi-Yau 4-fold under consideration or, equivalently, its dual periodic quiver. The crystals provide a discretized version of the underlying toric geometries. We introduce various techniques to visualize crystals and their melting configurations, including 3-dimensional slicing and Hasse diagrams. We illustrate the construction with the D0-D8 system on $\mathbb{C}^4$. Finally, we outline how our proposal generalizes to arbitrary toric CY 4-folds and general brane configurations.
Forward citations
Cited by 3 Pith papers
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Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
For quivers satisfying a no-overlap condition, flavored BPS indices are computed by crystal melting derived from Jeffrey-Kirwan residues, and new double quiver algebras are constructed whose crystal representations en...
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Quiver BPS Indices from Crystal Profiles
Elliptic genera and lower-dimensional BPS indices equal discrete sums over molecule boundaries in crystals defined by Jeffrey-Kirwan residues, generalizing Nekrasov Young-diagram formulas.
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Gauge Origami and BPS/CFT correspondence
The gauge origami partition function on C4 is realized as a correlation function of BPS qq-character operators, with D6 and D8 characters labeled by plane and solid partitions.
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