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

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 $\mathcal{W}$-algebra constraints.

arXiv comment18 pages, main author is Todor Milanov, appendix by Danilo Lewanski

References in corpus (1)

• The Eynard--Orantin recursion for the total ancestor potential

Cited by in corpus (2)

• Higher Airy structures and topological recursion for singular spectral curves
• A New Class of Higher Quantum Airy Structures as Modules of $\mathcal{W}({\mathfrak{gl}}_r)$-Algebras