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arXiv · 1603.00073

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

Todor Milanov·Danilo Lewanski
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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.

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Todor Milanov, Danilo Lewanski. 2016-02-29. $\mathcal{W}$-algebra constraints and topological recursion for $A_N$-singularity. https://arxiv.org/abs/1603.00073

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