Remodeling for binary-dihedral orbifold Gromov–Witten theory
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Can affine binary-dihedral orbifold Gromov–Witten invariants be recovered by involution-equivariant sign-sector recursion on a type-D logarithmic Toda curve? The target covers stable descendants with n>0 and 2g−2+n>0, and free energies with g≥2 on the specified smooth chamber.
Why it matters and what counts as progress
Why it matters: The binary-dihedral orbifold is non-toric, so the proposed correspondence extends remodeling beyond earlier toric Calabi–Yau settings.
What counts as progress: Prove the recursion correspondence in this non-toric setting or extend its chamber, genus or insertion scope.
How the problem developed
Bouchard, Klemm, Mariño, and Pasquetti Proposed the remodeling correspondence for toric Calabi–Yau threefolds, relating B-model topological recursion to higher-genus Gromov–Witten theory; the binary-dihedral target lies outside that toric setting.
Andrea Brini, Jingxiang Ma, and Ian A. B. Strachan Constructed the type-D logarithmic Toda B-model and identified its genus-zero mirror structure for ADE resolutions, supplying the surface-level input used by the later threefold work.
- 8 Jul 2026 · Reported claim [3]
Bohan Fang, Zhuoming Lan, and Jingxiang Ma The preprint claims closed-string remodeling for the affine binary-dihedral Calabi–Yau orbifold threefold, with stable descendants and equivariant free energies for genus g ≥ 2.
AI contribution
Involution-equivariant topological recursion and mirror symmetry for the affine binary dihedral Calabi--Yau threefold
Fang, Lan and Ma identify affine binary-dihedral orbifold Gromov–Witten theory with involution-equivariant sign-sector recursion on a type-D logarithmic Toda curve, for stable descendants with n>0 and 2g−2+n>0 and free energies with g≥2 on the stated smooth chamber.
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