Mathematical Research Letters

Volume 23 (2016)

Number 4

Fourier duality of quantum curves

Pages: 1111 – 1137



Martin T. Luu (Department of Mathematics, University of Illinois, Urbana-Champaign, Il., U.S.A.)

Albert Schwarz (Department of Mathematics, University of California, Davis, Calif., U.S.A.)


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.

Accepted 10 December 2015

Published 16 September 2016