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K-Theoretic DT/PT Correspondence for Toric Calabi–Yau 4-Folds

Cao, Yalong ; Kool, Martijn ; Monavari, Sergej

Communications in mathematical physics, 2022-11, Vol.396 (1), p.225-264 [Periódico revisado por pares]

Berlin/Heidelberg: Springer Berlin Heidelberg

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  • Título:
    K-Theoretic DT/PT Correspondence for Toric Calabi–Yau 4-Folds
  • Autor: Cao, Yalong ; Kool, Martijn ; Monavari, Sergej
  • Assuntos: Classical and Quantum Gravitation ; Complex Systems ; Mathematical and Computational Physics ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Reduction ; Relativity Theory ; Theoretical
  • É parte de: Communications in mathematical physics, 2022-11, Vol.396 (1), p.225-264
  • Descrição: Recently, Nekrasov discovered a new “genus” for Hilbert schemes of points on C 4 . We extend its definition to Hilbert schemes of curves and moduli spaces of stable pairs, and conjecture a K -theoretic DT/PT correspondence for toric Calabi–Yau 4-folds. We develop a K -theoretic vertex formalism, which allows us to verify our conjecture in several cases. Taking a certain limit of the equivariant parameters, we recover the cohomological DT/PT correspondence for toric Calabi–Yau 4-folds recently conjectured by the first two authors. Another limit gives a dimensional reduction to the K -theoretic DT/PT correspondence for toric 3-folds conjectured by Nekrasov–Okounkov. As an application of our techniques, we find a conjectural formula for the generating series of K -theoretic stable pair invariants of Tot P 1 ( O ( - 1 ) ⊕ O ( - 1 ) ⊕ O ) . Upon dimensional reduction to the resolved conifold, we recover a formula which was recently proved by Kononov–Okounkov–Osinenko.
  • Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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