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

Todor Milanov; Danilo Lewanski

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

Algebraic Geometry 2016-03-02 v1 High Energy Physics - Theory

Authors: Todor Milanov , Danilo Lewanski

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.

Cite

@article{arxiv.1603.00073,
  title  = {$\mathcal{W}$-algebra constraints and topological recursion for $A_N$-singularity},
  author = {Todor Milanov and Danilo Lewanski},
  journal= {arXiv preprint arXiv:1603.00073},
  year   = {2016}
}

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

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

Abstract

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