Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

By Z. Bern, J. J. Carrasco, L. Dixon, H. Johansson, R. Roiban. 2012

248 citations recorded by the source corpus.

We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/015f6fcfe7fb621dd84fd24ea2beb35321896005

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Citations in the corpus

Pure gravities via color-kinematics duality for fundamental matter (2014, methodology): “In this way, the triangle and the bubble numerators, shown in figure 10, are obtained from the box as ntri(1, 2, 3, 4, l) ≡ nbox ( [1, 2], 3, 4, l ) , nbub(1, 2, 3, 4, l) ≡ ntri ( 1, 2, [3, 4], l ) = nbox ( [1, 2], [3, 4], l ) .”
Color-kinematic duality for form factors (2012, methodology): “In the construction with color-kinematics duality, one also needs to consider the graphs with less loop propagators but with more complicated trivalent tree legs, for example, the “snail-like” diagrams [10].”
Double copy for massive quantum particles with spin (2019, background): “This duality is present in many physically relevant gauge theories, such as pure Yang-Mills theory [15, 17–19], quantum chromodynamics (QCD) [20–22], Yang-Mills-Higgs models [23], and supersymmetric generalizations thereof [16, 20, 23–28].”
Loops in AdS from conformal field theory (2016, methodology): “This has resisted years of direct attack using advanced methods [74–76].”
Color-kinematics duality for QCD amplitudes (2015, unknown): “23b) n7(1 , 2 + , 3, 4 + , 5, 6 + ) = −i ( 〈13〉[42]〈5|1+2|6] + 〈35〉[64]〈1|3+4|2] + 〈15〉[62]〈3|5+6|4] ) .”
Polylogarithms, multiple zeta values and superstring amplitudes (2013, background): “[2, 22, 23, 24] (and references therein) that color and kinematic contributions to gauge-theory amplitudes share their algebraic properties and are freely interchangeable.”
Black hole binary dynamics from the double copy and effective theory (2019, background): “n. This includes applying generalized unitarity [73{80] and double-copy constructions [81{83], which have enabled explicit (super)gravity calculations at remarkably high orders of perturbation theory [84,84{91]. The double copy allows us to express gravitational scattering amplitudes in terms of cor”
Colour-Kinematics duality for one-loop rational amplitudes (2013, methodology): “The four-point amplitude in N = 4 super-Yang-Mills (sYM) has been put into a form with numerators satisfying the duality up to four loops [2, 20, 21].”