Fourier duality of quantum curves
Martin Luu, Albert Schwarz
TL;DR
This paper explores the duality between two deformation methods of quantum curves within the KP hierarchy, revealing a local Fourier duality that connects them and applying this insight to duality results in 2D quantum gravity.
Contribution
It establishes a local Fourier duality linking two deformation approaches of quantum curves and provides a conceptual proof of duality in 2D quantum gravity.
Findings
The two KP orbits are related by a local Fourier duality.
A conceptual proof of duality results in 2D quantum gravity is provided.
Clarifies the relation between different quantum curve deformations.
Abstract
There are two different ways to deform a quantum curve along the flows of the KP hierarchy. We clarify the relation between the two KP orbits: In the framework of suitable connections attached to the quantum curve they are related by a local Fourier duality. As an application we give a conceptual proof of duality results in 2D quantum gravity.
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