The geometry of Nekrasov's gauge origami theory
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| Format: | Preprint |
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2026
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| _version_ | 1866908802212691968 |
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| author | Arbesfeld, Noah Kool, Martijn Lim, Woonam |
| author_facet | Arbesfeld, Noah Kool, Martijn Lim, Woonam |
| contents | Nekrasov's gauge origami theory provides a (complex) 4-dimensional generalization of the ADHM quiver and its moduli spaces of representations. We describe the origami moduli space as the zero locus of an isotropic section of a quadratic vector bundle on a smooth space. This allows us to give an algebro-geometric definition of the origami partition function in terms of Oh--Thomas virtual cycles. The key input is the computation of a sign associated to each torus fixed point of the moduli space. Furthermore, we establish an integrality result and dimensional reduction formulae, and discuss an application to non-perturbative Dyson--Schwinger equations following Nekrasov's work. Finally, we conjecture a description of the origami moduli space in terms of certain 2-dimensional framed sheaves on $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, which we verify at the level of torus fixed points. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_00984 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The geometry of Nekrasov's gauge origami theory Arbesfeld, Noah Kool, Martijn Lim, Woonam Algebraic Geometry High Energy Physics - Theory 14D20, 14D21, 14J60, 14N35, 16G20 Nekrasov's gauge origami theory provides a (complex) 4-dimensional generalization of the ADHM quiver and its moduli spaces of representations. We describe the origami moduli space as the zero locus of an isotropic section of a quadratic vector bundle on a smooth space. This allows us to give an algebro-geometric definition of the origami partition function in terms of Oh--Thomas virtual cycles. The key input is the computation of a sign associated to each torus fixed point of the moduli space. Furthermore, we establish an integrality result and dimensional reduction formulae, and discuss an application to non-perturbative Dyson--Schwinger equations following Nekrasov's work. Finally, we conjecture a description of the origami moduli space in terms of certain 2-dimensional framed sheaves on $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, which we verify at the level of torus fixed points. |
| title | The geometry of Nekrasov's gauge origami theory |
| topic | Algebraic Geometry High Energy Physics - Theory 14D20, 14D21, 14J60, 14N35, 16G20 |
| url | https://arxiv.org/abs/2602.00984 |