$\mathcal{W}$-algebra constraints and topological recursion for $A_N$-singularity

Todor Milanov; Danilo Lewanski

paper

$W$ -algebra constraints and topological recursion for $A_{N}$ -singularity

arXiv:1603.00073

Abstract

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 $W$ -algebra constraints.

18 pages, main author is Todor Milanov, appendix by Danilo Lewanski

W-algebra constraints and topological recursion for AN​-singularity

Abstract

$W$ -algebra constraints and topological recursion for $A_{N}$ -singularity