The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory

C. Vergu

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The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory

C. Vergu

High Energy Physics - Theory · Submitted 17 Aug 2009

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The authors' main claim We compute the even part of the planar two-loop MHV amplitude in N=4 supersymmetric Yang-Mills theory, for an arbitrary number of external particles.

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We compute the even part of the planar two-loop MHV amplitude in N=4 supersymmetric Yang-Mills theory, for an arbitrary number of external particles. The answer is expressed as a sum of conformal integrals.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the even part of the planar two-loop MHV amplitude in N=4 supersymmetric Yang-Mills theory, for an arbitrary number of external particles.	contribution 0.98	0.96	0.66	asserted 1.00
s1	The answer is expressed as a sum of conformal integrals.	result 0.82	0.87	0.31	asserted 1.00

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The paper

Original abstract

We compute the even part of the planar two-loop MHV amplitude in N=4 supersymmetric Yang-Mills theory, for an arbitrary number of external particles. The answer is expressed as a sum of conformal integrals.

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References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
hep-th 2010-08 conditional novelty 8.0 of 10

A recursive formula generates the all-loop integrand for planar N=4 SYM scattering amplitudes in a form that keeps the full Yangian symmetry manifest.
Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
hep-th 2025-12 conditional novelty 7.0 of 10

A general two-loop formula is obtained for all n-point 10d null polygon correlators in planar N=4 SYM, expressed in a conformal-integral basis and verified numerically at 11 points.
Prescriptive Unitarity
hep-th 2017-04 conditional novelty 7.0 of 10

A prescriptive unitarity method yields a strictly diagonal basis of three-loop integrands for all n-point N^kMHV amplitudes in planar N=4 SYM, with each coefficient a single field-theory residue.
The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
hep-th 2010-08 accept novelty 7.0 of 10

The full four-loop four-gluon amplitude of N=4 super-Yang-Mills is constructed as 50 loop integrals, and its ultraviolet behavior reveals that double-trace color terms diverge more weakly than single-trace terms.
An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
hep-ph 2009-11 conditional novelty 7.0 of 10

The authors derive the first fully analytic expression for the two-loop six-edged Wilson loop, equivalently the six-point remainder function, in planar N=4 super Yang-Mills, valid in general kinematics.

Show 2 more citing papers

Dual Superconformal Invariance, Momentum Twistors and Grassmannians
hep-th 2009-09 conditional novelty 7.0 of 10

Planar N=4 SYM tree amplitudes and box coefficients are generated by holomorphic delta-function contour integrals over a Grassmannian in momentum twistor space, making dual superconformal invariance manifest.
The Two-Loop Hexagon Wilson Loop in N = 4 SYM
hep-th 2010-03 accept novelty 6.0 of 10

The two-loop six-edged Wilson loop in planar N=4 SYM is evaluated analytically in general kinematics, yielding the six-point remainder function as an explicit uniform-weight-four Goncharov polylogarithm expression.

How the literature uses it

9 arXiv papers cite this in 14 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 10 sentences without a confident label

Cites it as background 4 papers

Important advances have made use of twistors, momentum twistor space and dual conformal symmetry (DCI) to provide an understanding of the integrand of the $n$-point, multiloop amplitudes, e.g. [ref] .

Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes · Introduction · 0.97
In (see also the earlier work [ref] ), it was guessed (and checked) that the $n$-particle MHV amplitude integrand could be represented as[Notice that we have dropped the typical notation indicating N$^(𝐤=0)$MHV degree in `$𝒜_n^(L)$', as no other helicity sectors will be considered in this work.]

Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder · Local Integrands for (Logarithms of) MHV Amplitudes · 0.95
In the case of massless scattering amplitudes, the determination of the two-loop MHV amplitude for any number of points [ref] was an important stepping stone for many later developments and discoveries.

Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons · Discussion · 0.98

What it cites · 21 sentences without a confident label

Contests 4 papers

Unfortunately the BDS ansatz was shown to break down (see Refs. [ref] ).

Comments on gluon scattering amplitudes via AdS/CFT · Introduction · contest 0.81
Unfortunately the BDS ansatz was shown to break down (see Refs. [ref] ).

The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude · Introduction · contest 0.81
Unfortunately the BDS ansatz was shown to break down (see Refs. [ref] ).

The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory · Introduction · contest 0.81

Uses the method or tool of 8 papers

The computation was done by using the unitarity method (see Refs. [ref] ).

One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits · Description of the computational procedure · 1.00
The computation was done by using the unitarity method (see Refs. [ref] ).

One-Loop Amplitudes for e^+ e^- to Four Partons · Description of the computational procedure · 1.00
The computation was done by using the unitarity method (see Refs. [ref] ).

Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes · Description of the computational procedure · 1.00

Compares with 1 paper

A computation of these integrals in dimensional regularization through the finite parts (of order $𝒪(ϵ^0)$) would be very interesting and would allow a comparison with the results of Ref. [ref] , where the corresponding Wilson loop computation was performed.

Two-Loop Polygon Wilson Loops in N=4 SYM · Discussion · 0.87

Cites as support 2 papers

Another important restriction which can be proposed on the basis of the results in Ref. [ref] is the absence of integrals containing higher polygons.

Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory · Description of the computational procedure · 0.98
This is supported by the one-loop computation in Ref. [ref] and also by the leg addition rule of Ref. [ref] .

One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits · Description of the computational procedure · 1.00

Cites as background 36 papers

Later, in Ref. [ref] , Bern, Dixon and Smirnov conjectured that a similar relation holds to all orders in perturbation theory, after performing a three-loop check.

Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond · Introduction · 0.81
The first steps towards answering this question were made in Ref. [ref] where Anastasiou, Bern, Dixon and Kosower discovered an iteration relation for the two-loop splitting functions and proposed that a similar relation holds for the MHV scattering amplitudes.

Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory · Introduction · 0.89
This symmetry was proposed and studied in a series of papers [ref] and it was later extended to a dual conformal supersymmetry in Ref. [ref] .

Conformal properties of four-gluon planar amplitudes and Wilson loops · Introduction · 0.91

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