Positivity of hexagon perturbation theory

The hexagon-form-factor program was proposed as a way to compute three-and higher-point correlation functions in super-symmetric Yang-Mills theory and in the dual AdS(5)xS(5) superstring theory, by exploiting the integrability of the theory in the 't Hooft limit. This approach is reminiscent of the asymptotic Bethe ansatz in that it applies to a large-volume expansion. Finite-volume corrections can be incorporated through Luscher-like formulae, though the systematics of this expansion is largely unexplored so far. Strikingly, finite-volume corrections may feature negative powers of the 't Hooft coupling g in the small-g expansion, potentially leading to a breakdown of the formalism. In this work we show that the finite-volume perturbation theory for the hexagon is positive and thereby compatible with the weak-coupling expansion for arbitrary n-point functions.