Resurgence structure to all orders of multi-bions in deformed SUSY quantum mechanics

2017/05/31 by Toshiaki Fujimori, Syo Kamata, Tatsuhiro Misumi +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Ground state #Imaginary time #Nonlinear system #Perturbation theory (quantum mechanics) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Semiclassical physics #Supersymmetric quantum mechanics #Supersymmetry #hep-th

paper · pdf · doi:10.1093/ptep/ptx101

published as Prog. Theor. Exp. Phys. (2017) 083B02 · 61 pages, 8 figures, references added, typos corrected

openalex created_date 2017/06/05 · openalex publication_date 2017/06/29 · arxiv created 2017/08/18 · arxiv updated 2017/08/23 · openalex updated_date 2026/08/05

Abstract

We investigate the resurgence structure in quantum mechanical models originating in 2d nonlinear 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 |δ ε|⁠, we derive exact results for the expansion coefficients. In the class of models described by real multiplets, the |\mathcal O(δε)| ground state energy has a non-Borel summable asymptotic series, which gives rise to imaginary ambiguities leading to rich resurgence structure. We discuss 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 |ℂ P^N-1| QM and show that the exact |\mathcal O(δε)| ground state energy can be completely reconstructed from the semiclassical multi-bion contributions. Although the |\mathcal O(δε)| ground state energy has trivial resurgence structure, a simple but rich resurgence structure appears at |\mathcal O(δε²)|⁠. We show the complete cancelation between the |\mathcal O(δε²)| 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 CP¹| QM.

Citations

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