Gluons and gravitons at one loop from ambitwistor strings

Abstract

We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions based on the scattering equations that were recently derived from ambitwistor string theory. We turn these expressions into explicit formulae depending only on the loop momentum, the external momenta and the external polarisations. These formulae are valid in any number of spacetime dimensions for pure Yang-Mills theory (gluon) and its natural double copy, NS-NS gravity (graviton, dilaton, B-field), and we also present formulae in four spacetime dimensions for pure gravity (graviton). We perform several tests of our results, such as checking gauge invariance and directly matching our four-particle formulae to previously known expressions. While these tests would be elaborate in a Feynman-type representation of the loop integrand, they become straightforward in the representation we use.

36 pages, 5 figures. v2: added references, published version

References in corpus (38)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• The Momentum Kernel of Gauge and Gravity Theories
• Evidence for a New Soft Graviton Theorem
• The Kinematic Algebra From the Self-Dual Sector
• Tensionless Strings and the Weak Gravity Conjecture
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Ambitwistor strings in 4-dimensions
• Soft sub-leading divergences in Yang-Mills amplitudes
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Subleading soft theorem in arbitrary dimension from scattering equations
• Scattering Amplitudes from Intersection Theory
• Yang-Mills origin of gravitational symmetries
• Scattering on plane waves and the double copy
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• 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
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• Perturbative gravity at null infinity
• Ambitwistor strings at null infinity and subleading soft limits
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Perturbative gauge theory at null infinity
• A Worldsheet Theory for Supergravity
• A "Twistor String" Inspired Formula For Tree-Level Scattering Amplitudes in N=8 SUGRA
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• Amplitudes on plane waves from ambitwistor strings
• One-loop monodromy relations on single cuts
• CHY-Graphs on a Torus
• Connecting the ambitwistor and the sectorized heterotic strings
• The complex null string, Galilean conformal algebra and scattering equations
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• A Gluing Operator for the Ambitwistor String

Cited by in corpus (39)

• Double copy for massive quantum particles with spin
• Type D Spacetimes and the Weyl Double Copy
• 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
• Plane wave backgrounds and colour-kinematics duality
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• One-loop Correlators and BCJ Numerators from Forward Limits
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• 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
• Integrands of loop amplitudes within loop-tree duality
• Superstring loop amplitudes from the field theory limit
• Loop amplitudes monodromy relations and color-kinematics duality
• Scalar-Graviton Amplitudes
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Transmuting CHY formulae
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-Loop Yang-Mills Integrands from Scattering Equations
• One-loop CHY-Integrand of Bi-adjoint Scalar Theory
• One-loop diagrams with quadratic propagators from the worldsheet
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• A Monte Carlo Approach to the 4D Scattering Equations
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• BCJ, worldsheet quantum algebra and KZ equations
• Bootstrapping solutions of scattering equations
• One-loop integrand from generalised scattering equations
• On differential operators and unifying relations for $1$-loop Feynman integrands
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes
• Advanced tools for basis decompositions of genus-one string integrals
• 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
• Ambitwistor strings and amplitudes in curved backgrounds