Analytic structure of then=7scattering amplitude inN=4SYM theory in multi-Regge kinematics: Conformal Regge cut contribution

Abstract

In this second part of our investigation [1] of the analytic structure of the 2 -> 5 scattering amplitude in the planar limit of f f = 4 super Yang-Mills theory in multi-Regge kinematics we compute, in all kinematic regions, the Regge-cut contributions at leading order. The results are infrared finite and conformally invariant.

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

“…While predictions for the latter to LLA have been worked out in [70][71][72], see also [69] for an extension to Ngluons, a major obstacle for their generalization to arbitrary logarithmic accuracy, is that the dispersion integral yielding the Regge cut contribution diverges when considering the N −1 LLA term at loops. This phenomenon is related to the fact that within the BFKL approach, the dual conformal invariance of the theory is not maintained at the intermediate steps of the calculation, and implies that some terms in the Regge pole contribution develop unphysical poles.…”

“…6 To make contact with other notations used in the literature, f+++ is denoted as fω 2 ω 3 in [71,72], and similarly the six-gluon analogue f++ of the previous section is denoted as fω 2 .…”

Heptagons from the Steinmann cluster bootstrap

“…With their help, we are able to fully determine the symbol of the seven-point three-loop NMHV and four-loop MHV amplitude in planar N = 4 SYM, using only a few simple physical and mathematical inputs. In a separate paper [60], we will investigate various kinematical limits of these amplitudes in more detail, including the multi-Regge limit [29,[61][62][63][64][65][66][67][68][69][70][71], the OPE limit [41][42][43][44][45][46][47][48], and the self-crossing limit [72,73]. In this paper, we study one of the simpler limits, where the NMHV seven-point amplitude factorizes on a multi-particle pole.…”

“…A full functional representation would be valuable for checking sevenpoint predictions in both the near-collinear [43][44][45][46][47][48][49][50] and multi-Regge limits [29,[61][62][63][64][65][66][67][68][69][70][71]. An important problem is to generalize the all-loop results for six-point scattering in the multi-Regge limit [110] to the seven-point case.…”

Hexagon OPE resummation and multi-Regge kinematics

“…The limit (3.2) has been studied in many papers (see for example [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]). In our preceding discussion from section 2 we were considering the double-scaling limit where one of the cross-ratios, u 2 was taken to zero.…”