The Gamma Conjecture of local mirror symmetry

Let $X$ be a noncompact toric Calabi–Yau variety and let $Y$ be its Hori–Vafa mirror. For mirror objects

$$E\in D^b\operatorname{Coh}(X)\leftrightarrow L\in Fuk(Y),$$

write $Z_t(E)$ for the central charge of $E$ and $C_t(L)$ for the central charge of $L$, as defined in the source's central-charge definitions. The Gamma Conjecture of local mirror symmetry. The central charges are equal:

$$Z_t(E)=C_t(L).$$

This conjecture proposes the local-mirror-symmetry analogue of the Gamma conjecture, expressing compatibility between central charges of mirror coherent sheaves and Lagrangian submanifolds. Its resolution status is not specified in the supplied text.