### 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, 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 language | English |
---|---|

Article number | 083B02 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2017 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2017 Aug 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2017*(8), [083B02]. https://doi.org/10.1093/ptep/ptx101

**Resurgence structure to all orders of multi-bions in deformed SUSY quantum mechanics.** / Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke.

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2017, no. 8, 083B02. https://doi.org/10.1093/ptep/ptx101

}

TY - JOUR

T1 - Resurgence structure to all orders of multi-bions in deformed SUSY quantum mechanics

AU - Fujimori, Toshiaki

AU - Kamata, Syo

AU - Misumi, Tatsuhiro

AU - Nitta, Muneto

AU - Sakai, Norisuke

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85050136951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050136951&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptx101

DO - 10.1093/ptep/ptx101

M3 - Article

AN - SCOPUS:85050136951

VL - 2017

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 8

M1 - 083B02

ER -