Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics

Understand

We investigate the resurgence structure in quantum mechanical models originating in 2d non-linear 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 $\delta \epsilon$, we derive exact results for the expansion coefficients.
• In the class of models described by real multiplets, the ${\mathcal O}(\delta\epsilon)$ ground state energy has a non-Borel summable asymptotic series, which gives rise to imaginary ambiguities leading to rich resurgence structure.
• We discuss the 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.