Miura operators, degenerate fields and the M2-M5 intersection

We determine the mathematical structures which govern the $\mathrm{\Omega }$ deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including degenerate modules, the Miura transform and Coulomb gas constructions. We give an algebraic interpretation of the Pandharipande-Thomas box counting in ${\mathbb{C}}^3$.