Yau's conjecture on the Strominger system through conifold transitions

Let $chat{X}$ be a Calabi–Yau threefold, and let

$$\hat{X} \rightarrow X_0 \rightsquigarrow X_t$$

be a conifold transition. Let $(\Omega_t,\omega_t,h_t)$ denote the holomorphic volume form, Hermitian form, and bundle metric involved in the Strominger system, and let $F_{h_t}$ and $R_{\omega_t}$ be the corresponding curvatures. Yau's conjecture. For small enough $t$, there exists a triple $(\Omega_t,\omega_t,h_t)$ solving the supersymmetry equations

$$,\quad,\quad$$

and the heterotic Bianchi identity

$$i \partial \bar{\partial} \omega_t = \alpha'_t \bigl(\operatorname{Tr}(F_{h_t} \wedge F_{h_t})-\operatorname{Tr}(R_{\omega_t} \wedge R_{\omega_t})\bigr),$$

where $R_\omega$ is the Chern curvature of $\omega$ and $\alpha'_t>0$. This is the conjectural completion of the authors' construction of solutions to the supersymmetry equations through conifold transitions; the additional Bianchi identity is required for the heterotic string equations and had not yet been solved through conifold transitions in the source.