Mathematical Research Letters
Volume 23 (2016)
Fourier duality of quantum curves
Pages: 1111 – 1137
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.