Refined Invariants and Quantum Curves from Supersymmetric Localization
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| Formato: | Preprint |
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2026
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| _version_ | 1866915723641618432 |
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| author | Banerjee, Sibasish Ishtiaque, Nafiz Jeong, Saebyeok |
| author_facet | Banerjee, Sibasish Ishtiaque, Nafiz Jeong, Saebyeok |
| contents | We study an Aganagic-Vafa brane supported on a special Lagrangian submanifold $\mathcal{L}$ in a non-compact toric Calabi-Yau threefold $\mathcal{X}$. From the perspective of geometric engineering, the Aganagic-Vafa branes give rise to a special class of half-BPS codimension-two defects in 5d $\mathcal{N}=1$ supersymmetric field theories in the presence of $Ω$-background. We propose that the defect partition functions give generating functions of refined, non-negative, integral open BPS invariants of the pair $(\mathcal{X},\mathcal{L})$, across different Kähler moduli chambers they are expanded in. In the Nekrasov-Shatashvili limit, the partition function provides a partially resummed solution to a $q$-difference equation that quantizes the mirror curve of $\mathcal{X}$ in an unambiguous fashion, in a polarization determined by the discrete labels of the Aganagic-Vafa brane. We demonstrate our method at examples of $\mathbb{C}^3$, resolved conifold, resolved $A_1$-singularity, local $F_0$, and local $F_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07662 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined Invariants and Quantum Curves from Supersymmetric Localization Banerjee, Sibasish Ishtiaque, Nafiz Jeong, Saebyeok High Energy Physics - Theory Mathematical Physics Algebraic Geometry 81T30, 81R12 We study an Aganagic-Vafa brane supported on a special Lagrangian submanifold $\mathcal{L}$ in a non-compact toric Calabi-Yau threefold $\mathcal{X}$. From the perspective of geometric engineering, the Aganagic-Vafa branes give rise to a special class of half-BPS codimension-two defects in 5d $\mathcal{N}=1$ supersymmetric field theories in the presence of $Ω$-background. We propose that the defect partition functions give generating functions of refined, non-negative, integral open BPS invariants of the pair $(\mathcal{X},\mathcal{L})$, across different Kähler moduli chambers they are expanded in. In the Nekrasov-Shatashvili limit, the partition function provides a partially resummed solution to a $q$-difference equation that quantizes the mirror curve of $\mathcal{X}$ in an unambiguous fashion, in a polarization determined by the discrete labels of the Aganagic-Vafa brane. We demonstrate our method at examples of $\mathbb{C}^3$, resolved conifold, resolved $A_1$-singularity, local $F_0$, and local $F_1$. |
| title | Refined Invariants and Quantum Curves from Supersymmetric Localization |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry 81T30, 81R12 |
| url | https://arxiv.org/abs/2601.07662 |