AdS type IIB twist as BCOV theory with a sourced five-form

Let $\mathbb{C}^2=\{z_1=z_2=z_3=0\}\subset\mathbb{C}^5$ and let $r=\sqrt{|z_1|^2+|z_2|^2+|z_3|^2}$ be the radius normal to $\mathbb{C}^2$. Let $F\in\Omega^{3,2}(\mathbb{C}^5\setminus\mathbb{C}^2)$ be the five-form specified by the source, with coefficient $N$ in the AdS background. AdS twist conjecture. The twist of type IIB supergravity on the $AdS_5\times S^5$ background is BCOV theory on $\mathbb{C}^5\setminus\mathbb{C}^2$, with the field $F$ taking the displayed value

$$F=N\frac{3}{4i\pi^3}\,\mathrm{d}z_1\,\mathrm{d}z_2\,\mathrm{d}z_3\,r^{-6}\left(\overline z_1\,\mathrm{d}\overline z_2\,\mathrm{d}\overline z_3-\overline z_2\,\mathrm{d}\overline z_1\,\mathrm{d}\overline z_3+\overline z_3\,\mathrm{d}\overline z_1\,\mathrm{d}\overline z_2\right).$$

Here $F$ is equivalently characterized by $\overline\partial F=N\delta_{\mathbb{C}^2}$ with tempered distributional extension. The conjecture proposes that the RR five-form is the only non-metric component contributing to the twisted AdS background; this remains conjectural.