Gromov–Witten duality conjecture for étale gerbes

Let $cmathcal{Y}$ be a $G$-gerbe over a compact symplectic orbifold $cmathcal{B}$, and let $(cmathcal{\widehat{Y}},c)$ be its dual pair, where $c$ is the flat $U(1)$-gerbe defining the twist. Write $cmathcal{D}_{cmathcal{Y}}$ for the total descendant potential of $cmathcal{Y}$, and $cmathcal{D}_{cmathcal{\widehat{Y}},c}$ for the $c$-twisted total descendant potential of $cmathcal{\widehat{Y}}$. Gromov–Witten duality conjecture. After suitable changes of variables, there is an equality of generating functions

$$cmathcal{D}_{cmathcal{Y}}=cmathcal{D}_{cmathcal{\widehat{Y}},c}.$$

This is the Gromov–Witten-theoretic formulation of the proposed duality between an étale gerbe and its dual pair. The source presents it as a natural claim suggested by the conformal-field-theory conjecture; no resolution is supplied here.