Bulk-boundary OPE and deformation matching conjecture for branes

Let $X=\operatorname{Spec}(\mathcal A)$ be an affine scheme associated with an associative algebra $\mathcal A$, and let $\mathcal E$ and $\mathcal F$ be sheaves or branes on $X$. In the B-model, consider the pairing

$$H^0(X,\Lambda^iTX)\times \operatorname{Ext}_X^n(\mathcal E,\mathcal F)\longrightarrow H^i(\operatorname{gl}_n(\mathcal A),S^j\operatorname{gl}_n(\mathcal A)^*)\times \operatorname{Ext}_X^n(\mathcal E,\mathcal F)\longrightarrow \operatorname{Ext}_X^{n+i}(\mathcal E,\mathcal F).$$

Bulk-boundary deformation conjecture. Such a mathematical pairing should realize a bulk-boundary operator product expansion under deformation of the BRST operator, and mathematical or geometrical deformations of a sheaf should match physical deformations of the corresponding branes in the sigma model.

The claim proposes a correspondence between bulk polyvector fields, boundary Ext groups, and physical brane deformations. The source presents it as a natural conjecture but gives no verification or resolution, so its general validity remains open.