Closed-string mirror symmetry for dimer models
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911257485901824 |
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| author | Cho, Dahye Hong, Hansol Jin, Hyeongjun Lee, Sangwook |
| author_facet | Cho, Dahye Hong, Hansol Jin, Hyeongjun Lee, Sangwook |
| contents | For all punctured Riemann surfaces arising as mirror curves of toric Calabi--Yau threefolds, we show that their symplectic cohomology is isomorphic to the compactly supported Hochschild cohomology of the noncommutative Landau--Ginzburg model defined on the NCCR of the associated toric Gorenstein singularities. This mirror correspondence is established by analyzing the closed-open map with boundaries on certain combinatorially defined immersed Lagrangians in the Riemann surface, yielding a ring isomorphism. We give a detailed examination of the properties of this isomorphism, emphasizing its relationship to the singularity structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed-string mirror symmetry for dimer models Cho, Dahye Hong, Hansol Jin, Hyeongjun Lee, Sangwook Symplectic Geometry Representation Theory 53D37, 53D40 (Primary) 14A22 (Secondary) For all punctured Riemann surfaces arising as mirror curves of toric Calabi--Yau threefolds, we show that their symplectic cohomology is isomorphic to the compactly supported Hochschild cohomology of the noncommutative Landau--Ginzburg model defined on the NCCR of the associated toric Gorenstein singularities. This mirror correspondence is established by analyzing the closed-open map with boundaries on certain combinatorially defined immersed Lagrangians in the Riemann surface, yielding a ring isomorphism. We give a detailed examination of the properties of this isomorphism, emphasizing its relationship to the singularity structure. |
| title | Closed-string mirror symmetry for dimer models |
| topic | Symplectic Geometry Representation Theory 53D37, 53D40 (Primary) 14A22 (Secondary) |
| url | https://arxiv.org/abs/2511.06699 |