Hexagon OPE Resummation and Multi-Regge Kinematics

Abstract

We analyse the OPE contribution of gluon bound states in the double scaling limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We provide a systematic procedure for perturbatively resumming the contributions from single-particle bound states of gluons and expressing the result order by order in terms of two-variable polylogarithms. We also analyse certain contributions from two-particle gluon bound states and find that, after analytic continuation to the $2\to 4$ Mandelstam region and passing to multi-Regge kinematics (MRK), only the single-particle gluon bound states contribute. From this double-scaled version of MRK we are able to reconstruct the full hexagon remainder function in MRK up to five loops by invoking single-valuedness of the results.

29 pages, 3 figures, 4 ancillary files

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Cited by in corpus (27)

• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Heptagons from the Steinmann Cluster Bootstrap
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• The Double Pentaladder Integral to All Orders
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• How tropical are seven- and eight-particle amplitudes?
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Hexagon POPE: effective particles and tree level resummation
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar $\mathcal{N}=4$ SYM
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Systematics of the Multi-Regge Three-Loop Symbol
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• ABJM flux-tube and scattering amplitudes
• The Multi-Regge Limit from the Wilson Loop OPE
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Hexagon Bootstrap in the Double Scaling Limit