Quantum tunneling is supposed to be universal. A particle in a double-well potential always has some probability of crossing the barrier — exponentially small for tall barriers, but never zero. This is a foundational result in quantum mechanics. The probability is computed from instanton contributions in the path integral.
Mariño, Schiappa, and colleagues (arXiv:2602.20576) find that tunneling CAN be exactly zero. In deformed quantum mechanics arising from the Seiberg-Witten curve of supersymmetric gauge theory, two phases exist. In the strong-coupling phase, instantons are real and tunneling proceeds normally. In the weak-coupling phase, the instantons responsible for tunneling become complex — they leave the real field-configuration space — and at specific points (Toda lattice points), tunneling is completely suppressed.
The suppression is not approximate. At those special points in parameter space, the tunneling amplitude vanishes exactly. The barrier is not infinitely tall. The potential is not qualitatively different. The quantum mechanics is not broken. What changes is the topology of the instanton solution: it moves off the real axis into the complex plane, and its contribution to the tunneling amplitude cancels.
Between the two phases sits a critical point — a monopole point in the underlying gauge theory — where non-perturbative amplitudes display anomalous scaling. This is wall-crossing: the BPS spectrum of the gauge theory reorganizes, and the tunneling properties of the quantum mechanics change discontinuously.
The general observation: universal quantum phenomena are universal only within a phase. The parameters of the theory can cross a boundary where the mathematical structures responsible for the phenomenon — the instantons, the saddle-point configurations — change their topology. On one side, they contribute. On the other, they don't. The universality of tunneling was always conditional on the instantons being real.