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arXiv · 2312.16950

Log topological recursion through the prism of $x-y$ swap

Alexander Alexandrov·Boris Bychkov·Petr Dunin-Barkowski·Maxim Kazarian·Sergey Shadrin
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Abstract

We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal $x-y$ swap relation. This result provides a vast generalization and a proof of a very recent conjecture of Hock. It also uniformly explains (and conceptually rectifies) an approach to the formulas for the $n$-point functions proposed by Hock.

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Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin. 2023-12-28. Log topological recursion through the prism of $x-y$ swap. https://doi.org/10.1093/imrn%2Frnae213

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