## 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 |
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Article number | 083B02 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2017 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2017 Aug |

## ASJC Scopus subject areas

- Physics and Astronomy(all)