Positivity of hexagon perturbation theory

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 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.

v2: misprints corrected, further details on physical magnons added

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• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Hexagons and Correlators in the Fishnet Theory
• Decagon at Two Loops
• Three-point functions at strong coupling in the BMN limit
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• A study of integrable form factors in massless relativistic AdS_3
• On analytical perturbative solution of ABJM quantum spectral curve
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Polylogarithms from the bound state S-matrix
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• A study of integrable form factors in massless relativistic $Ad{S}_2$