Calabi-Yau Products: Graded Quivers for General Toric Calabi-Yaus

Abstract

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$(5-2m)$-branes for $m=0,\dots ,3$ 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.

arXiv comment39 pages, 15 figures

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• Some Open Questions in Quiver Gauge Theory
• Charge functions for odd dimensional partitions