One-loop amplitudes in Einstein-Yang-Mills from forward limits

Abstract

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as (super-)Yang-Mills with the so-called YM+${\varphi }^3$ theory -- pure Yang-Mills coupled to bi-adjoint scalars -- which we implement via one-loop Cachazo-He-Yuan formulae. The YM+${\varphi }^3$ building blocks are obtained from forward limits of tree-level input in external gluons and scalars, and we give the composition rules for any number of traces and orders in the couplings $g$ and $\kappa$. On the one hand, we spell out supersymmetry- and dimension-agnostic relations that reduce loop integrands of Einstein-Yang-Mills to those of pure gauge theories. On the other hand, we present four-point results for maximal and half-maximal supersymmetry where all supersymmetry cancellations are exposed. In the half-maximal case, we determine six-dimensional anomalies due to chiral hypermultiplets in the loop.

arXiv comment51 + 8 pages, 18 figures, submission includes an ancillary data file; v2: typos fixed, matches version to be published in JHEP

References in corpus (64)

• 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
• New Developments in FeynCalc 9.0
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Gravity as the Square of Gauge Theory
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Scattering Equations and KLT Orthogonality
• Massive Loop Amplitudes from Unitarity
• Ambitwistor strings and the scattering equations
• The Momentum Kernel of Gauge and Gravity Theories
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Explicit BCJ Numerators from Pure Spinors
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• One-loop amplitudes on the Riemann sphere
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Extensions of Theories from Soft Limits
• Infinite Tension Limit of the Pure Spinor Superstring
• From loops to trees by-passing Feynman's theorem
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Berends-Giele recursion for double-color-ordered amplitudes
• Berends-Giele recursions and the BCJ duality in superspace and components
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• New Relations for Einstein-Yang-Mills Amplitudes
• One-loop Scattering Equations and Amplitudes from Forward Limit
• Heterotic and bosonic string amplitudes via field theory
• Expansion of Einstein-Yang-Mills Amplitude
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Gluons and gravitons at one loop from ambitwistor strings
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• 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
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• 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
• CHY Loop Integrands from Holomorphic Forms
• From maximal to minimal supersymmetry in string loop amplitudes
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• 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
• Local BCJ numerators for ten-dimensional SYM at one loop
• One-Loop Yang-Mills Integrands from Scattering Equations
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms

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