Wilson loop OPE, analytic continuation and multi-Regge limit

Abstract

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N=4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the "collinear-Regge" limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N^3LLA and the N^4LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE.

37 pages, 5 figures, v2: references added, v3: published version, a computational error in eq.(5.32) corrected

References in corpus (17)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
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• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Comments on operators with large spin
• An Operator Product Expansion for Polygonal null Wilson Loops
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Exacting N=4 Superconformal Symmetry
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Heptagon Amplitude in the Multi-Regge Regime
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling

Cited by in corpus (4)

• Bootstrapping an NMHV amplitude through three loops
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Evaluating the 6-point Remainder Function Near the Collinear Limit