English

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 xyx-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 nn-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