The GLSM–Gromov–Witten correspondence conjecture

Let $\bar X_W$ be the orbifold target of the gauged linear sigma model, let $\Lambda_+$ be the positive Novikov subring, and let $\tilde\tau_g$ and $\tau_g$ denote the genus-$g$ GLSM and orbifold Gromov–Witten potentials, respectively. For $\alpha\in H_{\it CR}^*(\bar X_W;\Lambda_+)$, their derivatives encode the corresponding GLSM and Gromov–Witten invariants.

GLSM–Gromov–Witten correspondence conjecture. There is an element $\mathfrak c\in H_{\it CR}^*(\bar X_W;\Lambda_+)$ such that

$$\frac{\partial^n\tilde\tau_g}{\partial\alpha_1\cdots\partial\alpha_n}(0)=\frac{\partial^n\tau_g}{\partial\alpha_1\cdots\partial\alpha_n}(\mathfrak c).$$

This conjecture predicts that GLSM invariants are obtained from orbifold Gromov–Witten invariants by a bulk deformation determined by the single class $\mathfrak c$. The source presents this as an important proposed relation between the two CohFTs; no resolution is supplied here.