Colored BPS Pyramid Partition Functions, Quivers and Cluster Transformations

Understand

We investigate the connections between flavored quivers, dimer models, and BPS pyramids for generic toric Calabi-Yau threefolds from various perspectives.

• We introduce a purely field theoretic definition of both finite and infinite pyramids in terms of quivers with flavors.
• These pyramids are associated to the counting of BPS invariants for generic toric Calabi-Yau threefolds.
• We discuss how cluster transformations provide an efficient recursive method for computing pyramid partition functions and show that the recursion is equivalent to the multidimensional octahedron recurrence.