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

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