Wilson loop OPE, analytic continuation and multi-Regge limit

TL;DR

This paper investigates the connection between collinear and multi-Regge limits in N=4 super Yang-Mills theory, using analytic continuation and Wilson loop OPE to compute scattering amplitudes up to five loops, providing new predictions and insights.

Contribution

It introduces a method combining collinear expansion, analytic continuation, and OPE to analyze scattering amplitudes in the multi-Regge limit, extending results up to five loops and beyond.

Findings

Results agree with known four-loop calculations.

Five-loop predictions at NNLLA match existing data.

New predictions for N^3LLA and N^4LLA are provided.

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.