Genus-like expansion conjecture for the D3-brane path integral

Let $Y$ be a target space-time and let $Z_{D3}(Y)$ denote the path integral of a perturbative D3-brane theory, with contributions summed over fundamental closed orientable $4$-manifolds $X$ and integrated over morphisms from Azumaya manifolds $(X^{A\!z},{\cal E})$ to $Y$. Genus-like expansion conjecture. There exists a built-in natural genus-like expansion for the path integral $Z_{D3}(Y)$ of a perturbative D3-brane theory. This is motivated by the role of closed orientable $2$-manifolds and genus expansions in string path integrals, together with the proposed sum over fundamental $4$-manifolds for D3-branes; the source does not state a resolution.