New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

Abstract

In this letter, we extend the tree-level Kawai--Lewellen--Tye (KLT) and Bern--Carrasco--Johansson (BCJ) amplitude relations to loop integrands of gauge theory and gravity. By rearranging the propagators of gauge and gravity loop integrands, we propose the first manifestly gauge- and diffeomorphism invariant formulation of their double-copy relations. The one-loop KLT formula expresses gravity integrands in terms of more basic gauge invariant building blocks for gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop analogue of the BCJ relations, and both KLT and BCJ relations are universal to bosons and fermions in any number of spacetime dimensions and independent on the amount of supersymmetry. Also, one-loop integrands of Einstein--Yang--Mills (EYM) theory are related to partial integrands of pure gauge theories.

6 pages; v2: references added, minor corrections, published version with updated reference on work in progress

References in corpus (11)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Gravity and Yang-Mills Amplitude Relations
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New Relations for Einstein-Yang-Mills Amplitudes
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• New Identities among Gauge Theory Amplitudes
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills

Cited by in corpus (55)

• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Scattering Amplitudes from Intersection Theory
• Type D Spacetimes and the Weyl Double Copy
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Heterotic and bosonic string amplitudes via field theory
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Expansion of Einstein-Yang-Mills Amplitude
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Gluons and gravitons at one loop from ambitwistor strings
• The Double Pentaladder Integral to All Orders
• The double copy for heavy particles
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Plane wave backgrounds and colour-kinematics duality
• Unraveling conformal gravity amplitudes
• Tree-level amplitudes from the pure spinor superstring
• Double-Copy Structure of One-Loop Open-String Amplitudes
• 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
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Integrands of loop amplitudes within loop-tree duality
• Superstring loop amplitudes from the field theory limit
• One-loop monodromy relations on single cuts
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• 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
• Scattering Forms, Worldsheet Forms and Amplitudes from Subspaces
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Local BCJ numerators for ten-dimensional SYM at one loop
• One-Loop Yang-Mills Integrands from Scattering Equations
• KLT Factorization of Nonrelativistic String Amplitudes
• A double copy from twisted (co)homology at genus one
• One-loop diagrams with quadratic propagators from the worldsheet
• A scattering amplitudes approach to hard thermal loops
• One-loop CHY-Integrand of Bi-adjoint Scalar Theory
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• 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
• KLT Factorization of Winding String Amplitudes
• Advanced tools for basis decompositions of genus-one string integrals
• Note on solutions of scattering equations
• 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
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands