On the wall-crossing formula for quadratic differentials
Geometric Topology
2023-05-12 v2 High Energy Physics - Theory
Algebraic Geometry
Classical Analysis and ODEs
Abstract
We prove an analytic version of the Kontsevich-Soibelman wall-crossing formula describing how the number of finite-length trajectories of a quadratic differential jumps as the differential is varied. We characterize certain birational automorphisms of an algebraic torus appearing in this wall-crossing formula using Fock-Goncharov coordinates. As an application, we compute the Stokes automorphisms for the Voros symbols appearing in the exact WKB analysis of Schr\"odinger's equation.
Cite
@article{arxiv.2006.08059,
title = {On the wall-crossing formula for quadratic differentials},
author = {Dylan G. L. Allegretti},
journal= {arXiv preprint arXiv:2006.08059},
year = {2023}
}
Comments
37 pages. Version 2: Incorporated suggestions from referee