Degenerate and irregular topological recursion

Abstract

We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original topological recursion of Chekhov-Eynard-Orantin in the regular case and allows, in particular, to get meaningful answers in a variety of irregular and degenerate situations.

v3: 30 pages; several corrections, clarifications and comments added thanks to the remarks of the anonymous referees

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Cited by in corpus (6)

• Symplectic (Non-)Invariance of the Free Energy in Topological Recursion
• Taking limits in topological recursion
• GW/DT invariants and 5D BPS indices for strips from topological recursion
• Resonance transformations for the $(2,2p+1)$ minimal string via $x-y$ swap: a proof of Artemev's conjecture
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants
• Blobbed topological recursion and KP integrability