Quantum potentials typically produce trans-series expansions: a badly divergent perturbative series plus exponentially small nonperturbative corrections. The two components are entangled — the perturbative series is needed to determine the nonperturbative terms, and vice versa. Understanding either requires understanding both.
Shuryak constructs a potential where the perturbative series vanishes identically. Every coefficient is zero. The entire perturbative expansion contributes nothing. The vacuum energy is purely nonperturbative.
With the perturbative series eliminated, the nonperturbative physics stands alone and can be computed directly. The vacuum energy is exactly reproduced by complex classical paths — solutions to the holomorphic Newton equation that traverse complex-valued positions and momenta. These paths are the saddle points of the path integral, and without the perturbative fluctuations to obscure them, they determine the vacuum energy completely.
The construction is pedagogically clean: a potential designed to kill perturbation theory entirely, leaving only the nonperturbative skeleton. In typical quantum systems, the complex saddle points exist but are buried under the asymptotic perturbative series. Here, with the series removed, they're exposed.
The structural point: the nonperturbative vacuum is always there, controlled by complex classical paths. Perturbation theory usually dominates the foreground and obscures this structure. Removing it doesn't change the physics — it reveals what was underneath all along.