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A<sc>bstract</sc> 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.
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Calabi-Yau products: graded quivers for general toric Calabi-Yaus
A bstract The open string sector of the topological B-model on CY ( m + 2)-folds is described by m -graded quivers with superpotentials. This correspondence generalizes the connection between CY ( m + 2)-folds and gauge theories on the worldvolume of D(5 − 2 m )-branes for m = 0 , . . . , 3 to arbitrary m . In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CY m +2 and CY n +2 produces the quiver theory for a related CY m + n +3 . This method significantly supersedes existing ones, enabling the simple determination of quiver theories for geometries that were previously out of practical reach.
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- PAR ID:
- 10232609
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 2
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP02(2021)174
