Refined, Motivic, and Quantum

Understand

It is well known that in string compactifications on toric Calabi-Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content.

• In this paper we study how these invariants behave under wall crossing.
• In particular, by applying a refined wall crossing formula, we obtain the refined BPS degeneracies for the conifold in different chambers.
• The result can be interpreted in terms of a new statistical model that counts `refined' pyramid partitions; the model provides a combinatorial realization of wall crossing and clarifies the relation between refined pyramid partitions and the refined topological vertex.