One-loop Correlators and BCJ Numerators from Forward Limits

Abstract

We present new formulas for one-loop ambitwistor-string correlators for gauge theories in any even dimension with arbitrary combinations of gauge bosons, fermions and scalars running in the loop. Our results are driven by new all-multiplicity expressions for tree-level two-fermion correlators in the RNS formalism that closely resemble the purely bosonic ones. After taking forward limits of tree-level correlators with an additional pair of fermions/bosons, one-loop correlators become combinations of Lorentz traces in vector and spinor representations. Identities between these two types of traces manifest all supersymmetry cancellations and the power counting of loop momentum. We also obtain parity-odd contributions from forward limits with chiral fermions. One-loop numerators satisfying the Bern-Carrasco-Johansson (BCJ) duality for diagrams with linearized propagators can be extracted from such correlators using the well-established tree-level techniques in Yang-Mills theory coupled to biadjoint scalars. Finally, we obtain streamlined expressions for BCJ numerators up to seven points using multiparticle fields.

34+11 pages, 1 figure; v2: typos corrected; cosmetic improvements in appendix C and elsewhere

References in corpus (86)

• 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
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Gravity as the Square of Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Group theory factors for Feynman diagrams
• Scattering Equations and KLT Orthogonality
• Ambitwistor strings and the scattering equations
• Explicit BCJ Numerators from Pure Spinors
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Open & Closed vs. Pure Open String Disk Amplitudes
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• 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
• The Ultraviolet Properties of N=4 Supergravity at Four 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
• One-loop amplitudes on the Riemann sphere
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• The Duality Between Color and Kinematics and its Applications
• Extensions of Theories from Soft Limits
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Infinite Tension Limit of the Pure Spinor Superstring
• The closed-string 3-loop amplitude and S-duality
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• Gravity Amplitudes as Generalized Double Copies
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• Berends-Giele recursions and the BCJ duality in superspace and components
• String-inspired BCJ numerators for one-loop MHV amplitudes
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• One-loop Scattering Equations and Amplitudes from Forward Limit
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Expansion of Einstein-Yang-Mills Amplitude
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• New Representations of the Perturbative S-Matrix
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• Monodromy Relations in Higher-Loop String Amplitudes
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Gluons and gravitons at one loop from ambitwistor strings
• Higher-loop amplitude monodromy relations in string and gauge theory
• String predictions for near future colliders from one-loop scattering amplitudes around D-brane worlds
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Evaluation of the CHY Gauge Amplitude
• Elliptic scattering equations
• String amplitudes from field-theory amplitudes and vice versa
• Supersymmetry Relations Between Contributions To One-Loop Gauge Boson Amplitudes
• Algorithmic construction of SYM multiparticle superfields in the BCJ gauge
• $\Lambda$ Scattering Equations
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• 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
• Monodromy relations from twisted homology
• CHY Loop Integrands from Holomorphic Forms
• From maximal to minimal supersymmetry in string loop amplitudes
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• One-loop monodromy relations on single cuts
• CHY-Graphs on a Torus
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• On integrands and loop momentum in string and field theory
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Higher Loop Spin Field Correlators in Various Dimensions
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• String-Based Perturbative Methods for Gauge Theories
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• One-Loop Yang-Mills Integrands from Scattering Equations
• A Gluing Operator for the Ambitwistor String
• Anomalies without an action
• Fermionic one-loop amplitudes of the RNS superstring

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• Off-Shell Color-Kinematics Duality for Chern-Simons
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Superstring loop amplitudes from the field theory limit
• Loop amplitudes monodromy relations and color-kinematics duality
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Unitarity Cuts of the Worldsheet
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Color-kinematics duality from the Bern-Kosower formalism
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• One-loop diagrams with quadratic propagators from the worldsheet
• 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
• Next-to-MHV Yang-Mills kinematic algebra
• Properties of the Conformal Yangian in Scalar and Gauge Field Theories
• Note on solutions of scattering equations
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands