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We study BPS spectra of D-branes on local Calabi-Yau threefolds $\mathcal{O}(-p)\oplus\mathcal{O}(p-2)\to \mathbb{P}^1$ with $p=0,1$, corresponding to $\mathbb{C}^3/\mathbb{Z}_{2}$ and the resolved conifold.
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S. Cecotti and C. Vafa, On classification of N=2 supersymmetric theories
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S. Hosono, M.-H. Saito, and A. Takahashi, Relative Lefschetz action and BPS state counting
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M. Aganagic, A. Klemm, and C. Vafa, Disk instantons, mirror symmetry and the duality web
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D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory, I
2003
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D. Maulik, N. Nekrasov, A. Okounkov, and R. Pandharipande, Gromov-Witten theory and Donaldson-Thomas theory, II
2004
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math/0408266
S. H. Katz, Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds · 2004
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P. S. Aspinwall and S. H. Katz, Computation of superpotentials for D-branes
2006
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B. Young, Computing a pyramid partition generating function with dimer shuffling
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2014
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