The B-model R-matrix conjecture for primitive-form phases

Let W~:CNC\tilde W:\mathbb{C}^N\to\mathbb{C} be a hypersurface singularity, and let ζ\zeta_\infty and ζ0\zeta_0 be the two specified choices of primitive form. Write ZW~,ζ\mathcal{Z}_{\tilde W,\zeta_\infty} and ZW~,ζ0\mathcal{Z}_{\tilde W,\zeta_0} for the corresponding Saito–Givental partition functions. B-model R-matrix conjecture. There is an upper-triangular Givental group element R=R(z)R=R(z) such that, up to a linear change of variables,

R^ZW~,ζ=ZW~,ζ0.\hat R\cdot\mathcal{Z}_{\tilde W,\zeta_\infty}=\mathcal{Z}_{\tilde W,\zeta_0}.

This is stated as the B-side counterpart of the A-model R-matrix conjecture, conditional on the relevant CY–LG and LG–LG mirror-symmetry conjectures. The source does not state a resolution.

Sources & referencesView supporting material

Primary source

Alexey Basalaev and Nathan Priddis, “Givental-type reconstruction at a non-semisimple point”, arXiv:1605.07862 (2017).

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