On the wall-crossing formula for quadratic differentials

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 Schrödinger's equation.

37 pages. Version 2: Incorporated suggestions from referee

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces
• Analyticity and resurgence in wall-crossing formulas

Cited by in corpus (2)

• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces