The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops

Abstract

Infrared divergences in scattering amplitudes arise when a loop momentum $\ell$ 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 $\ell \parallel p$ 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.

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

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Cited by in corpus (45)

• The Amplituhedron
• Bootstrapping an NMHV amplitude through three loops
• Into the Amplituhedron
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Positive Amplitudes In The Amplituhedron
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Matter dependence of the four-loop cusp anomalous dimension
• Prescriptive Unitarity
• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
• Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality
• The Double Pentaladder Integral to All Orders
• Ten dimensional symmetry of N=4 SYM correlators
• Cutting Deep Into The Amplituhedron
• Generalised ladders and single-valued polylogarithms
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Systematics of the cusp anomalous dimension
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Building Bases of Loop Integrands
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• Perturbative correlation functions of null Wilson loops and local operators
• Prescriptive Unitarity with Elliptic Leading Singularities
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Higher loop mixed correlators in N=4 SYM
• Integrated negative geometries in ABJM
• All-loop cuts from the Amplituhedron
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Positivity Sectors and the Amplituhedron
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• 4-particle Amplituhedronics for 3-5 Loops
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• Anatomy of the Amplituhedron
• All-loop Mondrian Diagrammatics and 4-particle Amplituhedron
• All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
• Illustrations of Integrand-Basis Building at Two Loops
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions