| Speaker: | Zhaojie Xu (Southeast University, China) |
|---|---|
| Title: | Trans-series representation of Hofstadter's butterfly from non-perturbative topological strings |
| Date (JST): | Tue, Nov 25, 2025, 13:30 - 15:00 |
| Place: | Seminar Room A |
| Abstract: |
The quantum Seiberg-Witten curve of the 5d N=1 pure SYM or the quantum mirror curve of a specific local Calabi-Yau manifold, known as local F_0, share intriguing connections with both the relativistic Toda lattice and the Harper-Hofstadter model in condensed matter physics. In this talk, we focus on the latter connection, exploring the non-perturbative completion of the Harper-Hofstadter model’s perturbative energy series. We’ll demonstrate that resurgence techniques, while powerful, are not sufficient to capture the full non-perturbative effects, such as the band structure. By extracting information from the Hofstadter’s butterfly, a fractal pattern arising in the model, we propose a conjecture for the complete trans-series structure for the flux ϕ=2π/Q. This leads us to derive the exact WKB quantization conditions written in terms of Voros symbols. Finally we discuss generalizations to local P^2 and its corresponding quantum mechanical system. For the imaginary slices of local P^2, the spectrum of its quantum curve is non-Hermitian and exhibits Z_3 symmetry. Near the semiclassical regime, we can still obtain trans-series corrections to the perturbative series for the first few instanton orders. |
