4d crystal melting, toric Calabi-Yau 4-folds and brane brick models

4d crystal melting, toric Calabi-Yau 4-folds and brane brick models

Blog Article

Abstract We introduce a class of 4-dimensional crystal melting models that count the BPS bound state of Board Games 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 Clutch Component 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.