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arXiv · 1806.06051

Positivity of hexagon perturbation theory

Burkhard Eden·Yunfeng Jiang·Marius de Leeuw·Tim Meier·Dennis le Plat·Alessandro Sfondrini
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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 AdS$_5\times$S$^5$ 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 L\"uscher-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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Burkhard Eden, Yunfeng Jiang, Marius de Leeuw, Tim Meier, Dennis le Plat, Alessandro Sfondrini. 2018-06-15. Positivity of hexagon perturbation theory. https://doi.org/10.1007/jhep11(2018)097

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