Cross-Order Integral Relations from Maximal Cuts

Abstract

We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.

58 pages, 19 figures; v2 references added

References in corpus (159)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Scattering Amplitudes with Open Loops
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Multiloop integrals in dimensional regularization made simple
• Gluon scattering amplitudes at strong coupling
• Differential Equations for Two-Loop Four-Point Functions
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Transcendentality and Crossing
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Conformal collider physics: Energy and charge correlations
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• The Amplituhedron
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
• Magic identities for conformal four-point integrals
• One-Loop Amplitudes for e^+ e^- to Four Partons
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Automation of one-loop QCD corrections
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Local Integrals for Planar Scattering Amplitudes
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• One-Loop Corrections to Five-Gluon Amplitudes
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• A Duality For The S Matrix
• Automated One-Loop Calculations with GoSam
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Massive Loop Amplitudes from Unitarity
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Progress in One-Loop QCD Computations
• From polygons and symbols to polylogarithmic functions
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• On-Shell Methods in Perturbative QCD
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Assault on the NLO Wishlist: pp -> tt bb
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Precise Predictions for W + 4 Jet Production at the Large Hadron Collider
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Motivic Amplitudes and Cluster Coordinates
• D-dimensional unitarity cut method
• One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Y-system for Scattering Amplitudes
• Towards a Basis for Planar Two-Loop Integrals
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Scattering into the fifth dimension of N=4 super Yang-Mills
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• The Grassmannian Origin Of Dual Superconformal Invariance
• One-Loop Amplitudes Of Gluons In SQCD
• Bootstrapping an NMHV amplitude through three loops
• Soft triple-real radiation for Higgs production at N3LO
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Uniqueness of two-loop master contours
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• The S-Matrix in Twistor Space
• Hexagon functions and the three-loop remainder function
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• The Cut-Constructible Part of QCD Amplitudes
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Direct Extraction Of One Loop Rational Terms
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Analytic two-loop form factors in N=4 SYM
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Scattering Amplitudes from Multivariate Polynomial Division
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• On soft singularities at three loops and beyond
• Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
• Maximal Unitarity at Two Loops
• Webs in multiparton scattering using the replica trick
• Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• The cusp anomalous dimension at three loops and beyond
• The infrared structure of gauge theory amplitudes in the high-energy limit
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Generalized Unitarity and Six-Dimensional Helicity
• Recursive Calculation of One-Loop QCD Integral Coefficients
• On Triple-Cut of Scattering Amplitudes
• The Yangian origin of the Grassmannian integral
• Loop amplitudes in gauge theories: modern analytic approaches
• NGluon: A Package to Calculate One-loop Multi-gluon Amplitudes
• On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Optimizing the Reduction of One-Loop Amplitudes
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Integral Coefficients for One-Loop Amplitudes
• Closed-Form Decomposition of One-Loop Massive Amplitudes
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• Twistor-Strings, Grassmannians and Leading Singularities
• One-loop amplitudes for W+3 jet production in hadron collisions
• The last of the simple remainders
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• From multiple unitarity cuts to the coproduct of Feynman integrals
• Local Spacetime Physics from the Grassmannian
• Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons
• On the renormalization of multiparton webs
• Five-loop Konishi in N=4 SYM
• Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Two-Loop Maximal Unitarity with External Masses
• On Genera of Curves from High-loop Generalized Unitarity Cuts
• Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Elliptic Functions and Maximal Unitarity
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Polynomial Structures in One-Loop Amplitudes
• Susy Theories and QCD: Numerical Approaches
• Analytic Structure of Three-Mass Triangle Coefficients
• The classification of two-loop integrand basis in pure four-dimension
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Multivariate Residues and Maximal Unitarity
• Twistor transform of all tree amplitudes in N=4 SYM theory
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Nonperturbative scales in AdS/CFT
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Counting to one: reducibility of one- and two-loop amplitudes at the integrand level
• Maximal Unitarity for the Four-Mass Double Box
• Unitarity Cuts of Integrals with Doubled Propagators
• Global Residues and Two-Loop Hepta-Cuts
• Heptagon Amplitude in the Multi-Regge Regime
• Massive Nonplanar Two-Loop Maximal Unitarity
• A Surprise in the Amplitude/Wilson Loop Duality

Cited by in corpus (8)

• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Cuts of Feynman Integrals in Baikov representation
• Prescriptive Unitarity
• Scattering Equations and Global Duality of Residues
• The Polynomial Form of the Scattering Equations is an H-Basis
• MultivariateResidues: a Mathematica package for computing multivariate residues
• Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes