The Off-Shell Recursion for Gravity and the Classical Double Copy for currents

Abstract

We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fluctuations of generalised metric. The perturbative action and equations of motion (EoM) are derived to arbitrary order for pure gravity case. We then derive the graviton off-shell recursion, the gravity counterpart of the Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner method using the EoM of the perturbative DFT. We solve the recursion iteratively and obtain the graviton off-shell currents explicitly. We then discuss the classical double copy for the off-shell currents. We present the current KLT relation for gravity by extending the result proposed by Mizera and Skrzypek for the non-gravitational effective field theories. The relation represents graviton currents by squaring gluon currents with the KLT kernel up to gauge transformation and regular terms that do not have any pole. Finally we discuss the off-shell conservation of currents for nonlinear gauge choices.

arXiv comment38 pages; v2: minor changes and fixes; v3: references added, published version

References in corpus (89)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Planck 2018 results. X. Constraints on inflation
• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Gravity as the Square of Gauge Theory
• Background independent action for double field theory
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• The gauge algebra of double field theory and Courant brackets
• The Kinematic Algebra From the Self-Dual Sector
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Explicit BCJ Numerators from Pure Spinors
• Differential geometry with a projection: Application to double field theory
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Stringy differential geometry, beyond Riemann
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Algebras for Amplitudes
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• Gravitational Radiation from Color-Kinematics Duality
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Type D Spacetimes and the Weyl Double Copy
• Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Manifest Duality in Low-Energy Superstrings
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Gravity and Yang-Mills Amplitude Relations
• N=1 Supersymmetric Double Field Theory
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• On amplitudes in self-dual sector of Yang-Mills theory
• Berends-Giele recursion for double-color-ordered amplitudes
• Berends-Giele recursions and the BCJ duality in superspace and components
• Kerr-Schild Double Field Theory and Classical Double Copy
• Incorporation of fermions into double field theory
• S-duality and the Double Copy
• The Weyl Double Copy for Gravitational Waves
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Classical Solutions and their Double Copy in Split Signature
• New Identities among Gauge Theory Amplitudes
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• Topology and Wilson lines: global aspects of the double copy
• The Classical Double Copy of a Point Charge
• Covariant Color-Kinematics Duality
• Perturbiner Methods for Effective Field Theories and the Double Copy
• A double copy for asymptotic symmetries in the self-dual sector
• Twin Supergravities from Yang-Mills Squared
• Twofold Symmetries of the Pure Gravity Action
• On factorizations in perturbative quantum gravity
• Ehlers as EM duality in the double copy
• The Newman-Penrose Map and the Classical Double Copy
• Weyl doubling
• Hidden Simplicity of the Gravity Action
• Monopoles, shockwaves and the classical double copy
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• New heavenly double copies
• Gravity as the square of Yang-Mills?
• Massive Gravity from Double Copy
• A solution to the non-linear equations of D=10 super Yang-Mills theory
• Loop-Level Double-Copy for Massive Quantum Particles
• SD Perturbiner in YM+Gravity
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• $L_{\infty }$-algebras and the perturbiner expansion
• Twistor Space Origins of the Newman-Penrose Map
• Loop Amplitudes and Quantum Homotopy Algebras
• On the Lagrangian formulation of the double copy to cubic order
• Radiation of scalar modes and the classical double copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• $\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz
• Gravitationally dressed Parke-Taylor amplitudes
• The $L_{\infty }$ structure of gauge theories with matter
• Multiparticle solutions to Einstein's equations
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Perturbative Double Field Theory on General Backgrounds
• Exploring the geometry of supersymmetric double field theory
• Gravitational SD Perturbiner

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