The flavour-background quotient for collinear singularities

Consider the self-dual $\operatorname{Sp}(K)$ gauge theory with massless fermions in

$$\frac{ }{}$$

$\mathrm{F}_K\boxtimes\boxtimes\boxtimes$ and in $wedge^2_0\mathrm{F}_K$, in the presence of the background axion field and the background flavour gauge field satisfying the source equation. Let $\mathcal{A}^{N,K}_{\mathrm{Defect}}$ denote the chiral algebra of the coupled system.

Flavour-background quotient conjecture. Collinear singularities in this theory are given by the quotient of $\mathcal{A}^{N,K}_{\mathrm{Defect}}$ by the relation that sets all bulk operators to zero except that $gammawidetilde{\gamma}$ is set to $M(z)$.

This proposes a chiral-algebra description of collinear singularities in the presence of the specified flavour background. The source does not state a proof or a general resolution.