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Analytic structure of the $n = 7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
High Energy Physics - Theory · Submitted 9 Nov 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results are infrared finite and conformally invariant.
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In this second part of our investigation of the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. The results are infrared finite and conformally invariant.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this second part of our investigation of the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. | contribution 1.00 | 0.95 | 0.42 | asserted 1.00 |
| s1 | The results are infrared finite and conformally invariant. | result 0.98 | 0.87 | 0.23 | asserted 1.00 |
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The paper
Original abstract
In this second part of our investigation of the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. The results are infrared finite and conformally invariant.
Human review
References
How the literature uses it
17 arXiv papers cite this in 44 sentences
Papers citing it · 24 sentences without a confident label
Builds on it 1 paper
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This long cut has already been studied for the $2 →5$ amplitude, and we can simply recapitulate the discussion [ref] and apply to the long cut in the $t_2$ and $t_3$ channels.
Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N=4 SYM: conformal Regge pole and Regge cut contributions · The long cut · 0.97
Uses its method or tool 2 papers
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We will make use of the method developed in our previous papers on the 7-point function [ref] , and wewill proceed in several steps: (1) We describe the decomposition of the $2 →6$ scattering amplitude into a sum of several pieces, where each term, in accordance with the Steinman relations, is characterized by a maximal set of non-overlapping energy discontinuities.
Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N=4 SYM: conformal Regge pole and Regge cut contributions · Outline of the strategy · 0.88
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In this paper, we compute through four loops all $2→5$ gluon scattering amplitudes in MRK with the non-trivial (“long”) Regge cut [ref] , by integrating along a sequence of paths connecting a known boundary point to MRK, using the iterated derivatives and boundary conditions obtained in Ref. [ref] .
Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics · Introduction · 0.83
Compares with it 3 papers
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In this final subsection, we will compare our findings for the 4-loop NMHV heptagon in MRK with independent results obtained for the latter to LLA [ref] and NLLA [ref] , based on the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach [ref] .
Cluster adjacency and the four-loop NMHV heptagon · Comparison with BFKL approach and new predictions · 1.00
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([ref]) already slightly differs from the predicted valued $δ_7,—$ in [ref] by an additional piece.
Regge meets collinear in strongly-coupled $\mathcal{N} = 4$ super Yang-Mills · Subleading kinematics for the $2→5$ – amplitude · 0.86
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This choice differs from the normalization used in [ref] by a factor of $2i$.]
Systematics of the Multi-Regge Three-Loop Symbol · Background · 0.96
Cites it as support 1 paper
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This is supported by all known results for remainder functions in MRK [ref] as well as the relation between the OPE in the near collinear limit and MRK [ref] .
All two-loop MHV remainder functions in multi-Regge kinematics · Discussion · 1.00
Cites it as background 11 papers
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While some partial results are known in particular for $n=7$, see e.g. [ref] and references therein, the scattering problem of $=4$ SYM theory with more than six gluons has not been solved.
The Two-Loop Symbol of all Multi-Regge Regions · Introduction · 0.88
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The first expressions for the multi-Regge limit of the heptagon remainder function in LLA and in all Mandelstam regions were proposed by Bartels in [ref] .
The Multi-Regge Limit from the Wilson Loop OPE · Introduction · 0.92
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In the seven-point case, the interesting Mandelstam regions have been classified and the corresponding dispersion integrals in LLA have been constructed in [ref] , which in turn were evaluated up to five loops in [ref] for the MHV case.
Regge meets collinear in strongly-coupled $\mathcal{N} = 4$ super Yang-Mills · Introduction · 0.83
What it cites · 33 sentences without a confident label
Builds on 1 paper
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In this second part of our investigation [ref] of the analytic structure of the $2→5$ scattering amplitude in the planar limit of $𝒩=4$ SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order.
Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution · Introduction · 0.95
Uses the method or tool of 1 paper
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They can be derived from the phases in ([ref]) and the pole pieces in ([ref]); in [ref] we found a slightly simpler way of calculation.
Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution · A digression: the $2→4$ scattering amplitude · 0.82
Uses data or values from 1 paper
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We combine these Regge cut results with the Regge poles which are taken from [ref] : τ_2τ_4: e^-iπ(ω_1+ω_3)e^iπω_a[e^iπ(ω_b+ω_c) - 2ie^iπω_3Ω_b Ω_c/Ω_3 ] = e^-iπ(ω_1+ω_3)e^iπω_a [cosπ(ω_b-ω_c) . . +i sinπ(ω_b+ω_c)- 2icosπω_3Ω_bΩ_c/Ω_3 ] τ_2τ_3τ_4: -e^-iπω_1e^iπω_a[e^-iπ(ω_b+ω_c) + 2ie^-iπω_3Ω_b Ω_c/Ω_3 ] = -e^-iπω_1e^iπω_a[cosπ(ω_b-ω_c). . -i sinπ(ω_b+ω_c)+ 2icosπω_3Ω_bΩ_c/Ω_3 ].
Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution · The $2 →5$ scattering amplitudes in different kinematic regions · 0.95
Compares with 1 paper
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Our phase $δ_13$ coincides with the phase contained in th BDS amplitude [ref] .
BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes · A digression: the $2→4$ scattering amplitude · 1.00
Cites as background 24 papers
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Details are described in [ref] .
Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution · Analytic structure and trigonometric coefficients · 0.85
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To illustrate our future strategy we briefly return to the well-studied case of the $2 →4$ scattering [ref] .
Analytic properties of high energy production amplitudes in N=4 SUSY · A digression: the $2→4$ scattering amplitude · 0.80
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The function $R_6$ has been calculated for two, three loops [ref] , four loops [ref] and even several attempts have been made for $n=7$ case up to two loops [ref] .
Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory · Introduction · 0.87
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