Log topological recursion through the prism of $x-y$ swap
Mathematical Physics
2025-01-22 v3 High Energy Physics - Theory
Algebraic Geometry
Combinatorics
math.MP
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 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 -point functions proposed by Hock.
Keywords
Cite
@article{arxiv.2312.16950,
title = {Log topological recursion through the prism of $x-y$ swap},
author = {Alexander Alexandrov and Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Shadrin},
journal= {arXiv preprint arXiv:2312.16950},
year = {2025}
}
Comments
32 pages; several corrections and clarifications