Open mirror conjecture for (W5,mu5)(W_5,mu_5)

Let F0,1LG(τ)F^{\mathrm{LG}}_{0,1}(\tau) be the generating function of genus-zero open FJRW invariants of (W5,μ5)(W_5,\mu_5), and let TLG(t)\mathcal{T}^{\mathrm{LG}}(t) and IkLG(t)I^{\mathrm{LG}}_k(t) denote the LG disk potential and LG II-functions, respectively. Open mirror conjecture for (W5,μ5)(W_5,\mu_5). Under the mirror map

τ=I1LG(t)I0LG(t),\tau=\frac{I^{\mathrm{LG}}_1(t)}{I^{\mathrm{LG}}_0(t)},

one has

F0,1LG(τ)=TLG(t)I0LG(t).F^{\mathrm{LG}}_{0,1}(\tau)=\frac{\mathcal{T}^{\mathrm{LG}}(t)}{I^{\mathrm{LG}}_0(t)}.

This conjecture identifies the genus-zero open FJRW generating function with the analytically continued B-model disk potential, normalized by the fundamental LG period; the invariants and generating function were yet to be defined in the source.

Sources & referencesView supporting material

Primary source

Konstantin Aleshkin and Chiu-Chu Melissa Liu, “Open/closed Correspondence and Extended LG/CY Correspondence for Quintic Threefolds”, arXiv:2309.14628 (2025).

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