Twofold Symmetries of the Pure Gravity Action

Abstract

We recast the action of pure gravity into a form that is invariant under a twofold Lorentz symmetry. To derive this representation, we construct a general parameterization of all theories equivalent to the Einstein-Hilbert action up to a local field redefinition and gauge fixing. We then exploit this freedom to eliminate all interactions except those exhibiting two sets of independently contracted Lorentz indices. The resulting action is local, remarkably simple, and naturally expressed in a field basis analogous to the exponential parameterization of the nonlinear sigma model. The space of twofold Lorentz invariant field redefinitions then generates an infinite class of equivalent representations. By construction, all off-shell Feynman diagrams are twofold Lorentz invariant while all on-shell tree amplitudes are automatically twofold gauge invariant. We extend our results to curved spacetime and calculate the analogue of the Einstein equations. While these twofold invariances are hidden in the canonical approach of graviton perturbation theory, they are naturally expected given the double copy relations for scattering amplitudes in gauge theory and gravity.

24 pages

References in corpus (3)

• Double Field Theory
• Black holes and the double copy
• From Fake Supergravity to Superstars

Cited by in corpus (23)

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• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
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• Towards Color-Kinematics Duality in Generic Spacetimes
• Graviton scattering in self-dual radiative space-times
• Non-perturbative aspects of the self-dual double copy
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• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Double copy for Lagrangians at trilinear order
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Flavour-kinematics duality for Goldstone modes
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Exploration of a Singular Fluid Spacetime
• Warm Dark Matter from Higher-Dimensional Gauge Theories
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Quantum Off-Shell Recursion Relation