Five-point amplitudes in N=4 super-Yang-Mills theory and N=8 supergravity

By J. J. Carrasco, H. Johansson. 2011

228 citations recorded by the source corpus.

We present the complete integrands of five-point superamplitudes in N = 4 super-Yang-Mills theory and N = 8 supergravity, at one and two loops, for four-dimensional external states and D-dimensional internal kinematics. For N = 4 super-Yang-Mills theory we give the amplitudes for general gauge group - including all non-planar contributions. The results are constructed using integral diagrams that manifestly satisfy the conjectured duality between color and kinematics, providing additional nontrivial evidence in favor of the duality for multipoint and multiloop ampli- tudes. We determine the ultraviolet poles by integrating the amplitudes in the dimensions where logarithmic divergences first occur. We introduce new kinematic prefactors which offer a conve- nient decomposition of the external state structure of the nonplanar five-point amplitudes in the maximally supersymmetric theories to all loop orders.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2eca375319de3e1a8929f490a7e4316e57384638

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Citations in the corpus

The double copy: Bremsstrahlung and accelerating black holes (2016, background): “This extension remains conjectural, but it has been verified in highly nontrivial examples at multiloop level [4, 14–35].”
Color-kinematic duality for form factors (2012, methodology): “Color-dual numerators have been constructed explicitly at tree level for all multiplicities through a variety of methods [6–8], and at loop level in specific examples in N = 4 SYM for five points up to two loops [9] and for four points up to four loops [10].”
Pure gravities via color-kinematics duality for fundamental matter (2014, background): “Further antisymmetrization gives the numerators of snail- and tadpole-type graphs, shown in figure 11: nsnail(1, 2, 3, 4, l) ≡ nbox ( [[1, 2], 3], 4, l ) , ntadpole(1, 2, 3, 4, l) ≡ nbox ( [[1, 2], [3, 4]], l ) , nxtadpole(1, 2, 3, 4, l) ≡ nbox ( [[[1, 2], 3], 4], l ) .”
Scattering Amplitudes from Multivariate Polynomial Division (2012, methodology): “The first extension of the integrand reduction method beyond one-loop was proposed in [14], and it was used to reproduce the results of two-loop 5point planar and non-planar amplitudes in N = 4 SYM [15, 16].”
Colour-Kinematics duality for one-loop rational amplitudes (2013, background): “Similarly, the five-point N = 8 amplitude has been constructed via the double copy [22] at one and two loops.”
Type D spacetimes and the Weyl double copy (2018, unknown): “At loop level, the double copy has been extensively studied [17–31], but to date it is still a conjecture [27].”
TASI Lectures on Scattering Amplitudes (2017, background): “BCJ duality is proven at tree-level [100] and vigorously checked at higher loop [101, 102, 103, 104, 105, 106, 107].”
One-loop amplitudes on the Riemann sphere (2015, background): “A valid choice for the pentagon and box numerators was present in [51],”
Color-kinematics duality for QCD amplitudes (2015, methodology): “This structure has been used successfully for tree and loop amplitudes in massless gauge theories with and without supersymmetry, including massless QCD with no quarks [32, 40–51].”
The classical double copy for Taub–NUT spacetime (2015, background): “Follow-up work has examined loop-level amplitudes [3,12–30], form-factors [31], or alternative theories [32].”