Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics

Abstract

We investigate the resurgence structure in quantum mechanical models originating in 2d non-linear sigma models with emphasis on nearly supersymmetric and quasi-exactly solvable parameter regimes. By expanding the ground state energy in powers of a supersymmetry-breaking deformation parameter $\delta \epsilon$, we derive exact results for the expansion coefficients. In the class of models described by real multiplets, the $\mathcal{O}(\delta \epsilon )$ ground state energy has a non-Borel summable asymptotic series, which gives rise to imaginary ambiguities leading to rich resurgence structure. We discuss the sine-Gordon quantum mechanics (QM) as an example and show that the semiclassical contributions from complex multi-bion solutions correctly reproduce the corresponding part in the exact result including the imaginary ambiguities. As a typical model described by chiral multiplets, we discuss the $\mathbb{C}{P}^{N-1}$ QM and show that the exact $\mathcal{O}(\delta \epsilon )$ ground state energy can be completely reconstructed from the semiclassical multi-bion contributions. Although the $\mathcal{O}(\delta \epsilon )$ ground state energy has trivial resurgence structure, a simple but rich resurgence structure appears at $\mathcal{O}(\delta {\epsilon }^2)$. We show the complete cancellation between the $\mathcal{O}(\delta {\epsilon }^2)$ imaginary ambiguities arising from the non-Borel summable perturbation series and those in the semiclassical contributions of $N-1$ complex bion solutions. We also discuss the resurgence structure of a squashed $\mathbb{C}{P}^1$ QM.

61 pages, 8 figures, references added, typos corrected

References in corpus (15)

• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Instantons in the Higgs Phase
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Instanton constituents in the O(3) model at finite temperature
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Finite N from Resurgent Large N
• Neutral bions in the CP^{N-1} model for resurgence

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