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Closed-string mirror symmetry for dimer models
Dahye Cho, Hansol Hong, Hyeongjun Jin, Sangwook Lee
https://arxiv.org/abs/2511.06699 https://arxiv.org/pdf/2511.06699 https://arxiv.org/html/2511.06699
arXiv:2511.06699v1 Announce Type: new
Abstract: 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.
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