The A-model R-matrix conjecture for mirror Gromov–Witten and FJRW theories

Let X\mathcal{X} be a Calabi–Yau variety and let (W,Gmax)(W,G_{\max}) be a pair defining an FJRW theory. Suppose that the Gromov–Witten theory of X\mathcal{X} and the FJRW theory of (W,Gmax)(W,G_{\max}) are two mirror A-models of the same B-model. Let ZX(t)\mathcal{Z}^{\mathcal{X}}(\mathbf{t}) and Z(W,Gmax)\mathcal{Z}^{(W,G_{\max})} denote their partition functions, and let t~(t)\tilde{\mathbf{t}}(\mathbf{t}) be a linear change of variables. A-model R-matrix conjecture. There is an upper-triangular Givental action R=R(z)R=R(z) such that

R^ZX(t)=Z(W,Gmax)(t~(t)).\hat R\cdot\mathcal{Z}^{\mathcal{X}}(\mathbf{t})=\mathcal{Z}^{(W,G_{\max})}(\tilde{\mathbf{t}}(\mathbf{t})).

This is presented as an A-side analogue of the corresponding B-side relation between the two primitive-form phases. 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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