Abstract
The hexagon-form-factor program was proposed as a way to compute three-and higher-point correlation functions in \( \mathcal{N}=4 \) super-symmetric Yang-Mills theory and in the dual AdS5×S5 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 Lüscher-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.
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Eden, B., Jiang, Y., de Leeuw, M. et al. Positivity of hexagon perturbation theory. J. High Energ. Phys. 2018, 97 (2018). https://doi.org/10.1007/JHEP11(2018)097
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DOI: https://doi.org/10.1007/JHEP11(2018)097