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

Toshiaki Fujimori, Syo Kamata, Tatsuhiro Misumi, Muneto Nitta, Norisuke Sakai

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29 Citations (Scopus)


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, we derive exact results for the expansion coefficients. In the class of models described by real multiplets, the O(δ) 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 CP N −1 QM and show that the exact O(δ) ground state energy can be completely reconstructed from the semiclassical multi-bion contributions. Although the O(δ) ground state energy has trivial resurgence structure, a simple but rich resurgence structure appears at O(δ 2 ). We show the complete cancelation between the O(δ 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 CP 1 QM.

Original languageEnglish
Article number083B02
JournalProgress of Theoretical and Experimental Physics
Issue number8
Publication statusPublished - 2017 Aug

ASJC Scopus subject areas

  • General Physics and Astronomy


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