The double-loop algebra B-algebra Yangian conjecture

Let $U^{comb}_\delta(\mathscr O_\epsilon(\mathbb C^2)\otimes\mathfrak{gl}_N)$ carry the $\mathbb C^\times$-action induced by scaling the two coordinates of $\mathbb C^2$ with opposite weights. For a graded algebra $A=\bigoplus_i A^i$, define its $B$-algebra by

$$\mathcal B(A)=A^0/\left(\bigoplus_{i>0}A^iA^{-i}\right).$$

Yangian degeneration conjecture. There is an isomorphism

$$\mathcal B\left(U^{comb}_\delta(\mathscr O_\epsilon(\mathbb C^2)\otimes\mathfrak{gl}_N)\right)\cong Y(\mathfrak{gl}_N).$$

This conjecture predicts that the dimensional reduction of the five-dimensional quantum field theory recovers the Yangian. Its proof is not supplied in the paper.