Open-closed duality in higher genus and winding

Abstract

Let X be a toric Fano surface. Let π: X̂ → X be a toric blow up at a point. We use the Topological Vertex [AKMV] to prove a higher genus, higher winding, open-closed duality between the toric Calabi-Yau 3-folds K_X, K_X̂. For g ≥ 0, w ≥ 1, we show the equality n_g(K_X̂, π^*β− wC) = (−1)^g N_{g, (w)}^LMOV(K_X/L, β), where n_g(K_X̂, π^*β− wC) is the genus-g, Gopakumar-Vafa invariant of K_X̂ in curve class π^*β−wC, where β∈ H₂(X, ℤ) and C is the exceptional curve, and N_{g, (w)}^LMOV(K_X/L, β) is the genus-g, LMOV invariant of an outer Aganagic-Vafa brane L ⊂ K_X in class β and representation (w), or the Young Tableau of a single row with w boxes.

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Cite

BibTeX RIS

BibTeX

@misc{zhou2026openclosed,
  title = {{Open-closed duality in higher genus and winding}},
  author = {Benjamin Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05926},
  eprint = {2609.05926},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05926},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Open-closed duality in higher genus and winding
AU  - Benjamin Zhou
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05926
UR  - https://arxiv.org/abs/2609.05926
AB  - Let X be a toric Fano surface. Let π: X̂ → X be a toric blow up at a point. We use the Topological Vertex [AKMV] to prove a higher genus, higher winding, open-closed duality between the toric Calabi-Yau 3-folds K_X, K_X̂. For g ≥ 0, w ≥ 1, we show the equality n_g(K_X̂, π^*β− wC) = (−1)^g N_g, (w)^LMOV(K_X/L, β), where n_g(K_X̂, π^*β− wC) is the genus-g, Gopakumar-Vafa invariant of K_X̂ in curve class π^*β−wC, where β∈ H_2(X, ℤ) and C is the exceptional curve, and N_g, (w)^LMOV(K_X/L, β) is the genus-g, LMOV invariant of an outer Aganagic-Vafa brane L ⊂ K_X in class β and representation (w), or the Young Tableau of a single row with w boxes.
ER  -

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