Webs of W-algebras

Understand

We associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory.

• Y-algebras associated to trivalent junctions are identified with truncations of $\mathcal{W}_{1+\infty}$ algebra.
• Starting with Y-algebras as atomic elements, we describe gluing of Y-algebras analogous to that of the topological vertex.
• At the level of characters, the construction matches the one of counting D0-D2-D4 bound states in toric Calabi-Yau threefolds.