Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity

Abstract

We present the complete integrands of five-point superamplitudes in N=4 super-Yang-Mills theory and N=8 supergravity, at one and two loops, for four-dimensional external states and D-dimensional internal kinematics. For N=4 super-Yang-Mills theory we give the amplitudes for general gauge group -- including all non-planar contributions. The results are constructed using integral diagrams that manifestly satisfy the conjectured duality between color and kinematics, providing additional nontrivial evidence in favor of the duality for multipoint and multiloop amplitudes. We determine the ultraviolet poles by integrating the amplitudes in the dimensions where logarithmic divergences first occur. We introduce new kinematic prefactors which offer a convenient decomposition of the external state structure of the nonplanar five-point amplitudes in the maximally supersymmetric theories to all loop orders.

33 pages, 5 figures, 1 table, v2 minor clarifications and references added

References in corpus (44)

• New Relations for Gauge-Theory Amplitudes
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Minimal Basis for Gauge Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Explicit BCJ Numerators from Pure Spinors
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• E7(7) constraints on counterterms in N=8 supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Basics of Generalized Unitarity
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Gravity and Yang-Mills Amplitude Relations
• Loop amplitudes in gauge theories: modern analytic approaches
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• 5 loops in 24/5 dimensions
• The vanishing volume of D=4 superspace
• Generic multiloop methods and application to N=4 super-Yang-Mills
• On duality symmetries of supergravity invariants
• Scattering amplitudes: the most perfect microscopic structures in the universe
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• New Identities among Gauge Theory Amplitudes
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• A Color Dual Form for Gauge-Theory Amplitudes
• Counterterms vs. Dualities
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• New Relations for Gauge-Theory Amplitudes with Matter
• Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
• Monodromy--like Relations for Finite Loop Amplitudes
• Virtuous Trees at Five and Six Points for Yang-Mills and Gravity
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• SUSY Ward identities, Superamplitudes, and Counterterms
• Note on New KLT relations
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• From lightcone actions to maximally supersymmetric amplitudes
• Holonomies of gauge fields in twistor space 3: gravity as a square of N=4 theory

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• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
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• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
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• Manifest colour-kinematics duality and double-copy in the string-based formalism
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• Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes
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• One-loop SYM-supergravity relation for five-point amplitudes
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• Positivity Sectors and the Amplituhedron
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
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