The quantum-field-theoretic deformation of differential-operator enveloping algebras

Let $\Sigma$ be an affine algebraic curve, and let $\operatorname{Diff}(\Sigma)$ be its algebra of polynomial differential operators. The five-dimensional quantum field theory on $\mathbb R\times T^*\Sigma$ has observables identified with cochains on $\mathfrak{gl}_N\otimes\operatorname{Diff}(\Sigma)$. Instanton large-charge conjecture. There is a deformation of

$$U(\mathfrak{gl}_N\otimes\operatorname{Diff}(\Sigma))$$

coming from this quantum field theory, describable as the large-$K$ limit of a deformation quantization of the moduli of instantons on $T^*\Sigma$. The conjecture extends the paper's large-charge description from specific surfaces to cotangent bundles of affine curves; its existence was stated as conjectural in the candidate, although the surrounding text indicates that the field-theoretic construction is available.