Tetrahedron instantons in Donaldson-Thomas theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929675574444032 |
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| author | Fasola, Nadir Monavari, Sergej |
| author_facet | Fasola, Nadir Monavari, Sergej |
| contents | Inspired by the work of Pomoni-Yan-Zhang in String Theory, we introduce the moduli space of tetrahedron instantons as a Quot scheme and describe it as a moduli space of quiver representations. We construct a virtual fundamental class and virtual structure sheaf à la Oh-Thomas, by which we define K-theoretic invariants. We show that the partition function of such invariants reproduces the one studied by Pomoni-Yan-Zhang, and explicitly determine it, as a product of shifted partition functions of rank one Donaldson-Thomas invariants of the three-dimensional affine space. Our geometric construction answers a series of questions of Pomoni-Yan-Zhang on the geometry of the moduli space of tetrahedron instantons and the behaviour of its partition function, and provides a new application of the recent work of Oh-Thomas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07145 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tetrahedron instantons in Donaldson-Thomas theory Fasola, Nadir Monavari, Sergej Algebraic Geometry High Energy Physics - Theory Inspired by the work of Pomoni-Yan-Zhang in String Theory, we introduce the moduli space of tetrahedron instantons as a Quot scheme and describe it as a moduli space of quiver representations. We construct a virtual fundamental class and virtual structure sheaf à la Oh-Thomas, by which we define K-theoretic invariants. We show that the partition function of such invariants reproduces the one studied by Pomoni-Yan-Zhang, and explicitly determine it, as a product of shifted partition functions of rank one Donaldson-Thomas invariants of the three-dimensional affine space. Our geometric construction answers a series of questions of Pomoni-Yan-Zhang on the geometry of the moduli space of tetrahedron instantons and the behaviour of its partition function, and provides a new application of the recent work of Oh-Thomas. |
| title | Tetrahedron instantons in Donaldson-Thomas theory |
| topic | Algebraic Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.07145 |