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We discuss a class of vertex operator algebras $\mathcal{W}_{m|n\times\infty}$ generated by a super-matrix of fields for each integral spin$1,2,3,\dots$. The algebras admit a large family of truncations that are incorrespondence with holomorphic functions on the Calabi-Yau singularity givenby solutions to $xy=z^mw^n$. We propose a free-field realization of suchtruncations generalizing the Miura transformation for $\mathcal{W}_N$ algebras.Relations in the ring of holomorphic functions lead to bosonization-likerelations between different free-field realizations. The discussion provides aconcrete example of a non-trivial interplay between vertex operator algebras,algebraic geometry and gauge theory.

On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities