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