$S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves
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arXiv
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| Natura: | Preprint |
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2026
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| author | Hristov, Kiril Kubo, Naotaka Pang, Yi |
| author_facet | Hristov, Kiril Kubo, Naotaka Pang, Yi |
| contents | We study the perturbative large-$N$ expansion of the round three-sphere partition function in a class of M2-brane theories, including flavored SYM and ABJM theories as well as more general 3d theories admitting dual $(p,q)$ 5-brane web descriptions. Using the Fermi gas formalism and quantum curve techniques, we derive the Airy-function representation of the partition function and find exact agreement with predictions based on equivariant constant maps in topological string theory proposed in [1]. In particular, we provide affirmative tests of this proposal for the toric geometries $\mathbb{C} \times \mathcal{C}$ (the conifold), the cone over the Sasakian space $Q^{1,1,1}$, and $\mathbb{C} \times \mathrm{SPP}$ (the suspended pinch point). Motivated by a recent conjecture in [2], we further propose a novel equivariant correspondence between distinct toric Calabi-Yau manifolds of the form $\mathrm{CY}_4 \leftrightarrow \mathbb{C} \times\mathrm{CY}_3$, arising from relations between the corresponding quantum curves under specific constraints. This correspondence suggests an equivariant extension and points toward a geometric origin of the topological string/spectral theory (TS/ST) correspondence, while offering new insight into the structure of the holographic duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves Hristov, Kiril Kubo, Naotaka Pang, Yi High Energy Physics - Theory We study the perturbative large-$N$ expansion of the round three-sphere partition function in a class of M2-brane theories, including flavored SYM and ABJM theories as well as more general 3d theories admitting dual $(p,q)$ 5-brane web descriptions. Using the Fermi gas formalism and quantum curve techniques, we derive the Airy-function representation of the partition function and find exact agreement with predictions based on equivariant constant maps in topological string theory proposed in [1]. In particular, we provide affirmative tests of this proposal for the toric geometries $\mathbb{C} \times \mathcal{C}$ (the conifold), the cone over the Sasakian space $Q^{1,1,1}$, and $\mathbb{C} \times \mathrm{SPP}$ (the suspended pinch point). Motivated by a recent conjecture in [2], we further propose a novel equivariant correspondence between distinct toric Calabi-Yau manifolds of the form $\mathrm{CY}_4 \leftrightarrow \mathbb{C} \times\mathrm{CY}_3$, arising from relations between the corresponding quantum curves under specific constraints. This correspondence suggests an equivariant extension and points toward a geometric origin of the topological string/spectral theory (TS/ST) correspondence, while offering new insight into the structure of the holographic duality. |
| title | $S^3$ partition functions and Equivariant CY$_4 $/CY$_3$ correspondence from Quantum curves |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.19159 |