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

2012/01/31 by Zvi Bern, Z. Bern, J. J. M. Carrasco +7 · 11 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Divergence (linguistics) #Duality (order theory) #Gauge anomaly #Gauge theory #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Seiberg duality #Supergravity #Supersymmetric gauge theory #Supersymmetry #Theoretical physics #Yang–Mills existence and mass gap #Yang–Mills theory #hep-th

paper · pdf · doi:10.1103/physrevd.85.105014

published as Phys.Rev. D85 (2012) 105014 · v2: PRD published version, fixed glitch in ancillary file. v1: 61 pages, 22 figures

openalex publication_date 2012/05/17 · arxiv created 2012/10/16 · arxiv updated 2012/10/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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_c² single-trace divergence in N=4 super-Yang-Mills theory.

Citations

• Three-loop leading singularities and Bern-Dixon-Smirnov ansatz for five particles
• Supersymmetry counterterms revisited
• Basics of generalized unitarity
• Explicit BCJ numerators from pure spinors
• On planar gluon amplitudes/Wilson loops duality
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• Exacting 𝒩 = 4 superconformal symmetry
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• Scattering amplitudes, Wilson loops and the string/gauge theory correspondence
• A note on the UV behaviour of maximally supersymmetric Yang–Mills theories
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Supersymmetric Yang-Mills theories
• Naturalness versus supersymmetric non-renormalization theorems
• Regularization and renormalization of gauge fields
• How Far Are We from the Quantum Theory of Gravity?
• Space–time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: exponentiation and Regge limits
• New relations for gauge-theory amplitudes

Cited by

• Inelastic black hole scattering from charged scalar amplitudes
• Little string amplitudes (and the unreasonable effectiveness of 6D SYM)
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• The structure of n-point one-loop open superstring amplitudes
• On the two-loop divergences in 6D, N=(1,1) SYM theory
• Higher-dimensional invariants in 6D super Yang-Mills theory
• Off- and on-shell harmonic superspaces for 6DSYM theories
• Curvature-squared multiplets, evanescent effects, and the U(1) anomaly in N=4 supergravity
• Radiative double copy for Einstein-Yang-Mills theory
• Unraveling conformal gravity amplitudes
• A vertex operator algebra construction of the colour-kinematics dual numerator
• Manifesting enhanced cancellations in supergravity: integrands versus integrals