On Chebyshev Wells: Periods, Deformations, and Resurgence

Abstract

We study the geometry and mechanics (both classical and quantum) of potential wells described by squares of Chebyshev polynomials. We show that in a small neighbourhood of the locus cut out by them in the space of hyperelliptic curves, these systems exhibit low-orders/low-orders resurgence, where perturbative fluctuations about the vacuum determine perturbative fluctuations about non-perturbative saddles.

arXiv commentv2: 36 pages, 2 figures, typos corrected, references added and discussion improved, matches version to appear in PRD

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• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension
• Pair Production in Real Proper Time and Unitarity Without Borel Ambiguity
• Triangle Groups: Automorphic Forms and Nonlinear Differential Equations