Genus one free energy contribution to the quartic Kontsevich model

2021/11/09 by Branahl, Johannes, Hock, Alexander
#05A15 #14H70 #14N10 #30F30 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2111.05411

Abstract

We prove a formula for the genus one free energy 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 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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