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

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.

arXiv comment32 pages; several corrections and clarifications

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• Symplectic (Non-)Invariance of the Free Energy in Topological Recursion
• GW/DT invariants and 5D BPS indices for strips from topological recursion
• The factorial growth of topological recursion
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants
• Blobbed topological recursion and KP integrability