Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics

We compute all 2 -> 5 gluon scattering amplitudes in planar N = 4 super- Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (long) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.

Automated summary

This paper computes all 2 -> 5 gluon scattering amplitudes in planar N = 4 super-Yang-Mills theory in the multi-Regge limit. The results are provided through four loops and to all logarithmic accuracy at leading power, represented in terms of single-valued multiple polylogarithms of two variables. By leveraging function-level results in the Steinmann cluster bootstrap, the authors find agreement with the recently conjectured all-order central emission vertex, providing a resummation of Fourier-Mellin residues into single-valued polylogarithms and an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.