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arXiv · 2503.15591

Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations

Hee-Cheol Kim·Minsung Kim·Sung-Soo Kim·Kimyeong Lee·Xin Wang
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Abstract

We investigate codimension-2 defect partition functions and quantum Seiberg-Witten curves in 5d rank-1 supersymmetric QFTs, including non-Lagrangian and Kaluza-Klein theories. Using generalized blowup equations, we compute defect partition functions in the $\Omega$-background and show that, in the Nekrasov-Shatashvili limit, they satisfy certain difference equations that encode the quantization of classical Seiberg-Witten curves. Furthermore, we explore novel transitions in the defect partition functions and their relation to coordinate transformations of quantum Seiberg-Witten curves, with a focus on SL(2,$\mathbb{Z}$) transformations and Hanany-Witten transitions. These findings provide new insights into the interplay between codimension-2 defects, quantum curves, and the geometric structure of 5d supersymmetric QFTs.

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Hee-Cheol Kim, Minsung Kim, Sung-Soo Kim, Kimyeong Lee, Xin Wang. 2025-03-19. Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations. https://doi.org/10.1007/jhep12(2025)080

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