$\mathcal{W}$-algebra constraints and topological recursion for   $A_N$-singularity
  We derive a Bouchard--Eynard type topological recursion for the total descendant potential of $A_N$-singularity. Our argument relies on a certain twisted representation of a Heisenberg Vertex Operator Algebra (VOA) constructed via the periods of $A_N$-singularity. In particular, our approach allows us to prove that the topological recursion for the total descendant potential is equivalent to a certain generating set of $\mathcal{W}$-algebra constraints. 
Todor Milanov and Danilo Lewanski
math.AG hep-th