The six-point remainder function to all loop orders in the multi-Regge limit

Abstract

We present an all-orders formula for the six-point amplitude of planar maximally supersymmetric N=4 Yang-Mills theory in the leading-logarithmic approximation of multi-Regge kinematics. In the MHV helicity configuration, our results agree with an integral formula of Lipatov and Prygarin through at least 14 loops. A differential equation linking the MHV and NMHV helicity configurations has a natural action in the space of functions relevant to this problem---the single-valued harmonic polylogarithms introduced by Brown. These functions depend on a single complex variable and its conjugate, w and w*, which are quadratically related to the original kinematic variables. We investigate the all-orders formula in the near-collinear limit, which is approached as |w|->0. Up to power-suppressed terms, the resulting expansion may be organized by powers of log|w|. The leading term of this expansion agrees with the all-orders double-leading-logarithmic approximation of Bartels, Lipatov, and Prygarin. The explicit form for the sub-leading powers of log|w| is given in terms of modified Bessel functions.

25 pages, 1 figure

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Cited by in corpus (21)

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• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Star Integrals, Convolutions and Simplices
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• The BFKL equation, Mueller-Navelet jets and single-valued harmonic polylogarithms
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Systematics of the Multi-Regge Three-Loop Symbol
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar $\mathcal{N}=4$ SYM
• A Two-Loop Four-Point Form Factor at Function Level
• The Multi-Regge Limit from the Wilson Loop OPE