Yangian module structure conjecture for superspin-chain sigma models

Let $m,n,L$ be positive integers, let $\mathbf{M}=(M_1,\dotsc,M_{m+n-1})\in\mathbb{Z}_{\geq0}^{m+n-1}$, and let $\CM(\mathbf{M})$ be the Calabi–Yau target of the corresponding effective sigma model. Let $T$ be the maximal torus of $\mathrm{GL}(L)^{m+n}\times\mathrm{GL}(1)$, and let the spin-chain sites carry Verma modules for $\mathfrak{gl}(m|n)$, with highest weights determined by the mass parameters. Yangian module structure conjecture. The direct sum

$$\bigoplus_{\mathbf{M}\in\mathbb{Z}_{\geq0}^{m+n-1}}H_T\bigl(\CM(\mathbf{M})\bigr)$$

is a module over $Y(\mathfrak{gl}(m|n))$, isomorphic to the tensor product of $L$ evaluation modules obtained from the Verma modules. This expresses the expected identification between the equivariant-cohomological state space of the A-model and the state space of the corresponding closed rational superspin chain. The source presents this as a mathematical conjecture, and no resolution is supplied.