Refined, Motivic, and Quantum |
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Authors: | Tudor Dimofte and Sergei Gukov |
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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. |
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