Wall-crossing for invariants of equivariant 3CY categories
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| Format: | Preprint |
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2025
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| _version_ | 1866918265179078656 |
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| author | Kuhn, Nikolas Liu, Henry Thimm, Felix |
| author_facet | Kuhn, Nikolas Liu, Henry Thimm, Felix |
| contents | We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694, using the authors' symmetrized pullback technique to preserve the symmetry of the (almost-perfect) obstruction theories throughout. As an application, we define and study wall-crossings of simple type between operational equivariant Donaldson--Thomas (DT), Pandharipande--Thomas (PT), and Bryan--Steinberg (BS) vertices. In particular, we give an explicit DT/PT descendent vertex correspondence in the Calabi--Yau limit. As another application, we construct and prove wall-crossing formulas for operational refined semistable Vafa--Witten invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wall-crossing for invariants of equivariant 3CY categories Kuhn, Nikolas Liu, Henry Thimm, Felix Algebraic Geometry High Energy Physics - Theory 14N35 We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694, using the authors' symmetrized pullback technique to preserve the symmetry of the (almost-perfect) obstruction theories throughout. As an application, we define and study wall-crossings of simple type between operational equivariant Donaldson--Thomas (DT), Pandharipande--Thomas (PT), and Bryan--Steinberg (BS) vertices. In particular, we give an explicit DT/PT descendent vertex correspondence in the Calabi--Yau limit. As another application, we construct and prove wall-crossing formulas for operational refined semistable Vafa--Witten invariants. |
| title | Wall-crossing for invariants of equivariant 3CY categories |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35 |
| url | https://arxiv.org/abs/2512.23012 |