On the Lagrangian formulation of the double copy to cubic order

Abstract

We investigate the Lagrangian formulation of the double-copy correspondence between gauge theories and gravity, up to the cubic order. Building on the definition of the double-copy field as a convolution of two vectors, we obtain free gravitational Lagrangians as products of two Yang-Mills Lagrangians, in a form amenable to be easily extended to the massive case. We discuss the origin of these results from tensionless strings and show the existence of gauge fixings that mix the two spin-one sectors and lead to an alternative, especially simple, version of the free Lagrangian. We then construct cubic vertices for the full double-copy multiplet, comprising a graviton, a two-form and a scalar particle, by means of the Noether procedure. Both at the free and at the cubic level the result gets uniquely fixed only upon imposing, on top of gauge invariance, a left-right Lorentz symmetry ruling contraction of indices among double-copy fields. Whereas the outcome nicely matches the cubic interactions of $\mathcal{N}=0$ supergravity, including the gauge-invariant coupling between the scalar particle and the two-form, such a twofold Lorentz symmetry seems to conflict with the perturbative reconstruction of space-time geometry.

arXiv comment28 pages. minor editing, matches published version

References in corpus (88)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Double Field Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Superspace Duality in Low-Energy Superstrings
• Self-Interaction and Gauge Invariance
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Gravity as the Square of Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Black holes and the double copy
• The Momentum Kernel of Gauge and Gravity Theories
• On higher spins and the tensionless limit of String Theory
• 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
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Transverse Fierz-Pauli symmetry
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• On the geometry of higher-spin gauge fields
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• 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
• Type D Spacetimes and the Weyl Double Copy
• A generating function for the cubic interactions of higher spin fields
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• Symmetry and Action for Flavor-Kinematics Duality
• BCJ duality and the double copy in the soft limit
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Higher-Spin Interactions: four-point functions and beyond
• Bound states and the classical double copy
• Perturbative Gravity from QCD Amplitudes
• Gravity as Gauge Theory Squared: A Ghost Story
• The Kinematic Algebras from the Scattering Equations
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• Exact solutions for the biadjoint scalar field
• Kerr-Schild Double Field Theory and Classical Double Copy
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Maxwell-like Lagrangians for higher spins
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• The Classical Double Copy of a Point Charge
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• The convolutional double copy: a case study with a point
• Cubic interactions of Maxwell-like higher spins
• Extended solutions for the biadjoint scalar field
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Are all supergravity theories Yang-Mills squared?
• Twofold Symmetries of the Pure Gravity Action
• Twin Supergravities from Yang-Mills Squared
• Gravitational radiation from the classical spinning double copy
• On factorizations in perturbative quantum gravity
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Hidden Simplicity of the Gravity Action
• String theory triplets and higher-spin curvatures
• Transverse Invariant Higher Spin Fields
• Biadjoint wires
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Curved Extended Superspace from Yang-Mills Theory a la Strings
• Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Massive Gravity from Double Copy
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• The Double Copy Structure of Soft Gravitons
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• Unimodular gravity with external sources
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• On the gauge symmetries of Maxwell-like higher-spin Lagrangians
• Gauge $\times$ Gauge on Spheres
• Generalised connections and higher-spin equations
• $\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• Low-spin models for higher-spin Lagrangians
• The double copy: gravity from gluons
• From polarized gravitational waves to analytically solvable electromagnetic beams
• The B-field soft theorem and its unification with the graviton and dilaton
• Unfree gauge symmetry in the Hamiltonian formalism
• Hamiltonian constraints and unfree gauge symmetry

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• Double Field Theory as the Double Copy of Yang-Mills
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• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
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• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Solutions in Nonlinear Electrodynamics and their double copy regular black holes
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Double copy for Lagrangians at trilinear order
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• Classical double copy and higher-spin fields
• The Weyl double copy from twistor space
• NS-NS Spacetimes from Amplitudes