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

Abstract

We investigate the analytic structure of the 2 → 5 production amplitude in the planar limit of N = 4 SYM in the multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities that have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the Bern-Dixon-Smirnov formula, to conformal invariant "renormalized" Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the 2 → 5 production amplitude.

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 .…”

“…7 See for example [71], where δ7 → δ14 is expressed in terms of the transverse momenta of the produced gluons, and the momentum transfer between them. It can be recast in terms of (transverse) cross ratios by virtue of the kinematic analysis of [70], as adapted to our conventions in [69].…”

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.…”

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.…”