Unified genus-1 potential and a parametric perturbative/nonperturbative relation
arXiv:2311.17850 · doi:10.1103/PhysRevD.110.125001
Abstract
We study a parametric deformation of the unified genus-1 anharmonic potential and derive a parametric form of perturbative/nonperturbative (P/NP) relation, applicable across all parameter values. We explicitly demonstrate that the perturbative expansion around the perturbative saddle is sufficient to generate all the nonperturbative information in these systems. Our results confirm the known results in the literature, where the cubic and quartic anharmonic potentials are reproduced under extreme parameter values, and go beyond these known results by developing the nonperturbative function of real and complex instantons solely from perturbative data.
16 pages, 5 figures, minor corrections, published version
References in corpus (32)
- Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
- A Primer on Resurgent Transseries and Their Asymptotics
- An Introduction to Resurgence, Trans-Series and Alien Calculus
- Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
- Uniform WKB, Multi-instantons, and Resurgent Trans-Series
- Generating Non-perturbative Physics from Perturbation Theory
- Resurgence theory, ghost-instantons, and analytic continuation of path integrals
- Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
- Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
- Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
- Complexified path integrals, exact saddles and supersymmetry
- Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
- Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
- Deconstructing zero: resurgence, supersymmetry and complex saddles
- Non-perturbative Contributions from Complexified Solutions in Models
- Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
- Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
- Bion non-perturbative contributions versus infrared renormalons in two-dimensional models
- Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
- The grin of Cheshire cat resurgence from supersymmetric localization
- Holomorphic Anomaly and Quantum Mechanics
- RG-Whitham dynamics and complex Hamiltonian systems
- On exact-WKB analysis, resurgent structure, and quantization conditions
- Remark on the Dunne-Unsal relation in exact semi-classics
- Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on
- Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
- WKB Method and Quantum Periods beyond Genus One
- Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D field theories
- The Picard-Fuchs equation in classical and quantum physics: Application to higher-order WKB method
- A resurgence analysis for cubic and quartic anharmonic potentials
- Exact instanton transseries for quantum mechanics
- All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability