The soft-collinear bootstrap: N = 4 Yang-Mills amplitudes at six- and seven-loops

2011/12/31 by Jacob L. Bourjaily, A. DiRe, Alexander DiRe +4 · 76 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Combinatorics #Conformal map #Conformal symmetry #Conjecture #Gauge theory #Gravitational singularity #Invariant (physics) #Logarithm #Loop (graph theory) #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Particle physics theoretical and experimental studies #Physics #Planar #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering amplitude #hep-th

paper · pdf · doi:10.1007/jhep03(2012)032

published in Journal of High Energy Physics 2012(3) (Springer Nature) · 27 pages, 48 figures, detailed results including PDF and Mathematica files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7 corrected, Lemma 2 removed

openalex publication_date 2012/03/01 · arxiv created 2014/11/24 · arxiv updated 2015/06/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Infrared divergences in scattering amplitudes arise when a loop momentum ℓ becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected behavior as ℓ ∥ p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively.

Citations

• Three-loop leading singularities and Bern-Dixon-Smirnov ansatz for five particles
• Sharpening The Leading Singularity
• Basics of generalized unitarity
• On planar gluon amplitudes/Wilson loops duality
• Two-Loop Iteration of Five-PointN=4Super-Yang-Mills Amplitudes
• Exacting 𝒩 = 4 superconformal symmetry
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Two-loop amplitudes of gluons and octa-cuts in Script N = 4 super Yang-Mills
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Are scattering amplitudes dual to super Wilson loops?
• From correlation functions to Wilson loops
• Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: exponentiation and Regge limits

Cited by

• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Building bases of loop integrands
• Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality inN=4Supersymmetric Yang-Mills Theory
• The double pentaladder integral to all orders

Related

• Symmetry properties of Wilson loops with a Lagrangian insertion
• Perturbative Correlation Functions and Scattering Amplitudes in Planar N=4 Supersymmetric Yang-Mills
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Maximal Super-Yang-Mills at Six Loops via Novel Integrand Bootstrap
• Hexagonal Wilson loop with Lagrangian insertion at two loops in N=4 super Yang-Mills theory