Abstract
We compute all 2 → 5 gluon scattering amplitudes in planar mathcal{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.
Highlights
Regge limit has been studied extensively in the context of perturbative quantum field theories
We compute all 2 → 5 gluon scattering amplitudes in planar N = 4 superYang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut
We compute through four loops all 2 → 5 gluon scattering amplitudes in multi-Regge kinematics (MRK) with the non-trivial (“long”) Regge cut [26, 35, 36], by integrating along a sequence of paths connecting a known boundary point to MRK, using the iterated derivatives and boundary conditions obtained in ref
Summary
In terms of Mandelstam invariants si,i+1 = (pi + pi+1) and si,i+1,i+2 = (pi + pi+1 + pi+2), the cross ratios are u1. Bosonic invariants are constructed from momentum twistor four-brackets, ijkl ≡ det(ZiZjZkZl). The MHV amplitude RM7 HV is free of Grassmann variables and is a single bosonic function of the cross ratios. It is invariant under the dihedral symmetry group D7, which includes cyclic transformations of order 7, and a reflection or flip. [17], RM7 HV = B7.) On the other hand, the NMHV amplitude RN7 MHV is a linear combination of five-brackets (2.10), with conformally invariant bosonic coefficients.
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