Counting surfaces on Calabi-Yau 4-folds II: $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence

Younghan Bae; Martijn Kool; Hyeonjun Park

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arXiv · 2402.06526

Counting surfaces on Calabi-Yau 4-folds II: $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence

Younghan Bae·Martijn Kool·Hyeonjun Park

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Abstract

This is the second part in a series of papers on counting surfaces on Calabi-Yau 4-folds. In this paper, we introduce $K$-theoretic $\mathrm{DT}, \mathrm{PT}_0, \mathrm{PT}_1$ invariants and conjecture a $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence. For certain tautological insertions, we derive Lefschetz principles in both the compact and toric case allowing reductions to 3-dimensional $\mathrm{DT}, \mathrm{PT}$ invariants. We also develop a topological vertex and conjecture a $\mathrm{DT}$-$\mathrm{PT}_0$ vertex correspondence. These methods enable us to verify our conjectures in several examples.

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Younghan Bae, Martijn Kool, Hyeonjun Park. 2024-02-09. Counting surfaces on Calabi-Yau 4-folds II: $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence. https://arxiv.org/abs/2402.06526

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