Resurgence and Holomorphy: From Weak to Strong Coupling

Understand

We analyze the resurgence properties of finite-dimensional exponential integrals which are prototypes for partition functions in quantum field theories.

• In these simple examples, we demonstrate that perturbation theory, even at arbitrarily weak coupling, fails as the argument of the coupling constant is varied.
• It is well-known that perturbation theory also fails at stronger coupling.
• We show that these two failures are actually intimately related.