The quantum-field-theoretic action on categorified Donaldson–Thomas invariants

Let $\mathcal M_{k,d,N,\alpha}$ be the relevant moduli space of quasi-maps, let $\mathcal P$ be the perverse sheaf lifting the Behrend-function data, and let $H^*_{\epsilon,\delta}(\mathcal M_{k,d,N,\alpha},\mathcal P)$ denote its equivariant cohomology. Let $A_{N,\delta,\epsilon}$ be the two-parameter combinatorial deformation of the enveloping algebra of differential operators with values in $\mathfrak{gl}_N$. Categorified Donaldson–Thomas action conjecture. The algebra $A_{N,\delta,\epsilon}$ acts on

$$\bigoplus_d H^*_{\epsilon,\delta}(\mathcal M_{k,d,N,\alpha},\mathcal P)$$

for all values of $k$ and $\alpha$. This predicts an algebraic action on the categorified Donaldson–Thomas cohomology of quasi-map spaces and is part of the proposed bridge between quantum field theory and enumerative geometry; no proof or resolution is given in the supplied text.