Perturbation theory approximates a solution by expanding around a known answer in powers of a small parameter. The series diverges — the coefficients grow so fast that summing all terms gives infinity rather than a finite answer. For decades, divergence was treated as a deficiency: the method breaks down, and you need something else to reach the non-perturbative regime.
Resurgence says the divergence is not a breakdown. It is information. Schwick (2026) constructs non-perturbative partition functions for the Virasoro minimal string and shows that negative-tension D-branes — non-perturbative objects that cannot appear at any finite order of perturbation theory — leave their signatures in the pattern of divergence of the perturbative series itself. The perturbative series knows about the non-perturbative objects. It encodes their properties in the specific way it fails to converge.
The mechanism is precise: the coefficients of the divergent series grow at rates controlled by the actions (energies) of the non-perturbative objects. A D-brane with action S produces a factorial growth in the perturbative coefficients that goes as n! × S^(-n). Different non-perturbative objects produce different growth patterns. Reading the divergence carefully — through Borel summation and lateral resummation — reconstructs the non-perturbative sector from the perturbative data alone. The failure and the knowledge are the same data.
The general principle: a method that appears to fail at its boundary can encode, in the pattern of its failure, exactly the information needed to extend it beyond that boundary. Divergence is not the absence of an answer. It is the answer in a form that requires a different reading.