Generalized mirror transformation for open Gromov–Witten invariants

Let $N$ and $k$ be the parameters of the projective hypersurface, let $P_f$ be the set of partitions $\sigma_f=(f_1,\ldots,f_{l(\sigma_f)})$ of $f$, and let

$$S(\sigma_f):=\prod_{i=1}^{f}\frac{1}{(\operatorname{mul}(i,\sigma_f))!}.$$

Here $w_{disk}^{N,k}({\cal O}_{h^a})_{2d-1}$ is the B-model disk amplitude, $\langle{\cal O}_{h^a}\rangle_{disk,2d-1}$ and the multipoint correlators are open Gromov–Witten invariants, and $w({\cal O}_{h^{N-3-(k-N)r}}{\cal O}_{h^0})_{0,r}$ is the quantity specified by the referenced formula. Generalized mirror transformation.

$$w_{disk}^{N,k}({\cal O}_{h^a})_{2d-1}=\langle{\cal O}_{h^a}\rangle_{disk,2d-1}+\sum_{f=1}^{d-1}\sum_{\sigma_f\in P_f}S(\sigma_f)\left\langle{\cal O}_{h^a}\prod_{j=1}^{l(\sigma_f)}{\cal O}_{h^{1+(k-N)f_j}}\right\rangle_{disk,2d-2f-1}\prod_{j=1}^{l(\sigma_f)}\frac{w({\cal O}_{h^{N-3-(k-N)f_j}}{\cal O}_{h^0})_{0,f_j}}{k}.$$

This is proposed as the open analogue of the closed generalized mirror transformation, translating B-model disk amplitudes into open Gromov–Witten invariants; the supplied parser status gives no evidence of resolution.