Generic multiloop methods and application to N=4 super-Yang-Mills

Abstract

We review some recent additions to the tool-chest of techniques for finding compact integrand representations of multiloop gauge-theory amplitudes - including non-planar contributions - applicable for N=4 super-Yang-Mills in four and higher dimensions, as well as for theories with less supersymmetry. We discuss a general organization of amplitudes in terms of purely cubic graphs, review the method of maximal cuts, as well as some special D-dimensional recursive cuts, and conclude by describing the efficient organization of amplitudes resulting from the conjectured duality between color and kinematic structures on constituent graphs.

42 pages, 18 figures, invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2 minor corrections, v3 added references

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Cited by in corpus (61)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Bootstrapping an NMHV amplitude through three loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Basics of Generalized Unitarity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Maximal Unitarity at Two Loops
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Gravity Amplitudes as Generalized Double Copies
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Double Copy from Homotopy Algebras
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Higher-loop amplitude monodromy relations in string and gauge theory
• Double-Copy Constructions and Unitarity Cuts
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
• Two-Loop Maximal Unitarity with External Masses
• An Introduction to On-shell Recursion Relations
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Loop-Level Double-Copy for Massive Quantum Particles
• Dual conformal symmetry at loop level; massive regularization
• Susy Theories and QCD: Numerical Approaches
• All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• SUSY Ward identities, Superamplitudes, and Counterterms
• Maximal Unitarity for the Four-Mass Double Box
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Graviton emission in Einstein-Hilbert gravity
• Cross-Order Integral Relations from Maximal Cuts
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes
• One-loop SYM-supergravity relation for five-point amplitudes
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• The four-loop six-gluon NMHV ratio function
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Group-theoretic relations for partial amplitudes in gauge theories with orthogonal group
• Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Generalized unitarity method for unstable particles
• Perturbative Gravity and Gauge Theory Relations -- A Review
• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Quantum point particle approximation of spinning black holes and compact stars
• Scattering Amplitudes in Gauge Theories
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity