2014/04/30 by Yasuyuki Hatsuda
Mathematics · Physics and Astronomy · #Amplitude #Analytic continuation #Asymptotic expansion #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Conjecture #Euclidean geometry #Gauge theory #Geometry #Interpolation (computer graphics) #Limit (mathematics) #Logarithm #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Scattering amplitude #Wilson loop #hep-th
paper · pdf · doi:10.1007/jhep10(2014)038
37 pages, 5 figures, v2: references added, v3: published version, a computational error in eq.(5.32) corrected
openalex publication_date 2014/10/01 · arxiv created 2015/03/31 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 N3LLA and the N4LLA 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.