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

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Cited by in corpus (22)

• Bootstrapping an NMHV amplitude through three loops
• 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
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Nonsinglet pentagons and NMHV amplitudes
• Fermionic pentagons and NMHV hexagon
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Resurgence of the Cusp Anomalous Dimension
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• On factorization of multiparticle pentagons
• The Two-Loop Symbol of all Multi-Regge Regions
• The four-loop six-gluon NMHV ratio function
• On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar $\mathcal{N}=4$ SYM
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Systematics of the Multi-Regge Three-Loop Symbol
• ABJM flux-tube and scattering amplitudes
• The Multi-Regge Limit from the Wilson Loop OPE