On the monodromy of the deformed cubic oscillator

Abstract

We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlev{é} equation. We use the generalised monodromy map for this equation to give solutions to the infinite-dimensional Riemann-Hilbert problems arising from the Donaldson-Thomas theory of the A2 quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.

arXiv comment68 pages. The appendix by the 2nd author. A few minor changes in this version

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Cited by in corpus (5)

• Null Kähler geometry and isomonodromic deformations
• A geometric recipe for twisted superpotentials
• Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies
• Spectral Networks and Non-abelianization
• Joyce structures on spaces of quadratic differentials