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.

28 pages. minor editing, matches published version

References in corpus (25)

• New Relations for Gauge-Theory Amplitudes
• Double Field Theory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Black holes and the double copy
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• 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
• The Kerr-Schild double copy in curved spacetime
• Yang-Mills origin of gravitational symmetries
• 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
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• The Classical Double Copy of a Point Charge
• Extended solutions for the biadjoint scalar field
• Twofold Symmetries of the Pure Gravity Action
• Transverse Invariant Higher Spin Fields
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• The Double Copy Structure of Soft Gravitons
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• Generalised connections and higher-spin equations
• The B-field soft theorem and its unification with the graviton and dilaton
• Unfree gauge symmetry in the Hamiltonian formalism

Cited by in corpus (14)

• Off-Shell Color-Kinematics Duality for Chern-Simons
• Double Field Theory as the Double Copy of Yang-Mills
• Asymptotic Weyl Double Copy
• Classical Spin Gravitational Compton Scattering
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Geodesics From Classical Double Copy
• Kinematic Hopf algebra for amplitudes and form factors
• 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
• Planar solutions of higher-spin theory. Nonlinear corrections
• Classical double copy and higher-spin fields
• NS-NS Spacetimes from Amplitudes