Paper
$S^3$ partition functions and Equivariant CY$_4 $/ CY$_3$ correspondence from Quantum curves
Authors
Kiril Hristov, Naotaka Kubo, Yi Pang
Abstract
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 holography duality.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.19159v1</id>\n <title>$S^3$ partition functions and Equivariant CY$_4 $/ CY$_3$ correspondence from Quantum curves</title>\n <updated>2026-03-19T17:14:35Z</updated>\n <link href='https://arxiv.org/abs/2603.19159v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.19159v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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 holography duality.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='hep-th'/>\n <published>2026-03-19T17:14:35Z</published>\n <arxiv:comment>71 pages, 11 figures</arxiv:comment>\n <arxiv:primary_category term='hep-th'/>\n <author>\n <name>Kiril Hristov</name>\n </author>\n <author>\n <name>Naotaka Kubo</name>\n </author>\n <author>\n <name>Yi Pang</name>\n </author>\n </entry>"
}