Refined, Motivic, and Quantum
arXiv:0904.1420 · doi:10.1007/s11005-009-0357-9
Abstract
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. We also compare the wall crossing behavior of the refined BPS invariants with that of the motivic Donaldson-Thomas invariants introduced by Kontsevich-Soibelman. In particular, we argue that, in the context of BPS state counting, the three adjectives in the title of this paper are essentially synonymous.
31 pages, 12 figures, harvmac
References in corpus (11)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- The Refined Topological Vertex
- Dimer models and toric diagrams
- Non-commutative Donaldson-Thomas theory and the conifold
- Crystal Melting and Toric Calabi-Yau Manifolds
- Wall crossing in local Calabi Yau manifolds
- Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
- Crossing the Wall: Branes vs. Bundles
- On the noncommutative Donaldson-Thomas invariants arising from brane tilings
- Computing a pyramid partition generating function with dimer shuffling
- Curve counting theories via stable objects I. DT/PT correspondence
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