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arXiv · 2111.05411

Genus one free energy contribution to the quartic Kontsevich model

Johannes Branahl·Alexander Hock
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Abstract

We prove a formula for the genus one free energy $\mathcal{F}^{(1)}$ of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blobbed topological recursion. We thus investigate the differences in $\mathcal{F}^{(1)}$ compared with its generic representation for ordinary topological recursion. In particular, we clarify the role of the Bergman $τ$-function in blobbed topological recursion. As a by-product, we show that considering the holomorphic additions contributing to $ω_{g,1}$ or not gives a distinction between the enumeration of bipartite and non-bipartite quadrangulations of a genus-$g$ surface.

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Johannes Branahl, Alexander Hock. 2021-11-09. Genus one free energy contribution to the quartic Kontsevich model. https://arxiv.org/abs/2111.05411

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