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

Fujimori, Toshiaki (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) ; Kamata, Syo (Physics Department and Center for Particle and Field Theory, Fudan University, 220 Handan Road, Yangpu District, Shanghai 200433, China) (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) ; Misumi, Tatsuhiro (Department of Mathematical Science, Akita University, 1-1 Tegata Gakuen-machi, Akita 010-8502, Japan) (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) (iTHEMS, RIKEN, 2-1 Hirasawa, Wako, Saitama 351-0198, Japan) ; Nitta, Muneto (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) ; Sakai, Norisuke (Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan) (iTHEMS, RIKEN, 2-1 Hirasawa, Wako, Saitama 351-0198, Japan)

11 August 2017

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 , we derive exact results for the expansion coefficients. In the class of models described by real multiplets, the 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 QM and show that the exact ground state energy can be completely reconstructed from the semiclassical multi-bion contributions. Although the ground state energy has trivial resurgence structure, a simple but rich resurgence structure appears at . We show the complete cancelation between the imaginary ambiguities arising from the non-Borel summable perturbation series and those in the semiclassical contributions of complex bion solutions. We also discuss the resurgence structure of a squashed QM.


Published in: PTEP 2017 (2017) 083B02
Published by: Oxford University Press/Physical Society of Japan
DOI: 10.1093/ptep/ptx101
arXiv: 1705.10483
License: CC-BY-3.0



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