New BCJ representations for one-loop amplitudes in gauge theories and gravity

Abstract

We explain a procedure to manifest the Bern-Carrasco-Johansson duality between color and kinematics in $n$-point one-loop amplitudes of a variety of supersymmetric gauge theories. Explicit amplitude representations are constructed through a systematic reorganization of the integrands in the Cachazo-He-Yuan formalism. Our construction holds for any nonzero number of supersymmetries and does not depend on the number of spacetime dimensions. The cancellations from supersymmetry multiplets in the loop as well as the resulting power counting of loop momenta is manifested along the lines of the corresponding superstring computations. The setup is used to derive the one-loop version of the Kawai-Lewellen-Tye formula for the loop integrands of gravitational amplitudes.

58 + 15 pages

References in corpus (74)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Super-Poincare Covariant Quantization of the Superstring
• Scattering of Massless Particles in Arbitrary Dimension
• Gravity as the Square of Gauge Theory
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Equations and KLT Orthogonality
• Explicit BCJ Numerators from Pure Spinors
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Open & Closed vs. Pure Open String Disk Amplitudes
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Consistency of Super-Poincare Covariant Superstring Tree Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Extensions of Theories from Soft Limits
• Multiple Elliptic Polylogarithms
• The closed-string 3-loop amplitude and S-duality
• R^4, purified
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Gravity and Yang-Mills Amplitude Relations
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• Gravity Amplitudes as Generalized Double Copies
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
• Berends-Giele recursion for double-color-ordered amplitudes
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
• One-loop Scattering Equations and Amplitudes from Forward Limit
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• A recursive method for SYM n-point tree amplitudes
• Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• New Representations of the Perturbative S-Matrix
• New Identities among Gauge Theory Amplitudes
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• Monodromy Relations in Higher-Loop String Amplitudes
• Integration Rules for Loop Scattering Equations
• Gluons and gravitons at one loop from ambitwistor strings
• Higher-loop amplitude monodromy relations in string and gauge theory
• Holography in Superspace
• String predictions for near future colliders from one-loop scattering amplitudes around D-brane worlds
• BCJ duality and double copy in the closed string sector
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Computation of Contour Integrals on ${\mathcal{M}}_{0,n}$
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation
• Elliptic scattering equations
• New relations for scattering amplitudes in Yang-Mills theory at loop level
• PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions
• Connected formulas for amplitudes in standard model
• CHY Loop Integrands from Holomorphic Forms
• CHY-Graphs on a Torus
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• One-loop four-graviton amplitudes in N=4 supergravity models
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• The two-loop superstring five-point amplitude and S-duality
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Anomalies without an action
• On the pole structures of the disconnected part of hyper elliptic g loop M point super string amplitudes

Cited by in corpus (63)

• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Type D Spacetimes and the Weyl Double Copy
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• The Sub-Leading Scattering Waveform from Amplitudes
• Heterotic and bosonic string amplitudes via field theory
• A new gauge-invariant double copy for heavy-mass effective theory
• Gluons and gravitons at one loop from ambitwistor strings
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Plane wave backgrounds and colour-kinematics duality
• Unraveling conformal gravity amplitudes
• Tree-level amplitudes from the pure spinor superstring
• Double copy structure of parity-violating CFT correlators
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• String amplitudes from field-theory amplitudes and vice versa
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• One-loop Correlators and BCJ Numerators from Forward Limits
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Conformal Gravity from Gauge Theory
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Integrands of loop amplitudes within loop-tree duality
• Superstring loop amplitudes from the field theory limit
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• One-loop monodromy relations on single cuts
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Scattering Forms, Worldsheet Forms and Amplitudes from Subspaces
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• On the New Factorizations of Yang-Mills Amplitudes
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-Loop Yang-Mills Integrands from Scattering Equations
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• One-loop diagrams with quadratic propagators from the worldsheet
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• BCJ, worldsheet quantum algebra and KZ equations
• Fermionic one-loop amplitudes of the RNS superstring
• BCJ Numerators from Differential Operator of Multidimensional Residue
• Basis decompositions of genus-one string integrals
• Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Pfaffian Diagrams for Gluon Tree Amplitudes
• Advanced tools for basis decompositions of genus-one string integrals
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Massive strings from a haunted field theory
• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands