Recently we have established a gauge theoretic construction of W-algebras, that we call the quiver W-algebras. In this construction, we obtain the q-deformed W-algebra associated with the quiver structure of 5d/K-theoretic gauge theory. Our formalism actually leads to a lot of new insights on W-algebras:
(i) Applying our formalism to the affine quiver gauge theory, the quiver W-algebra gives rise to double affinization of quantum algebra, which defines a new series of W-algebras.
(ii) We can consider 6d N = (1,0) quiver gauge theory compactified on a torus. In this case, we can construct the elliptic deformation of W-algebras.
(iii) Based on the connection between gauge theory and W-algebras, we have defined fractional quiver gauge theory, which describes non-simply-laced type quiver.