We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field. The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then construct an especially compact form for the Einstein-Hilbert action in which all graviton interactions are simply proportional to the graviton kinetic term. Our results apply to graviton perturbations about an arbitrary curved background spacetime.
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ArXiv ePrint: 1705.00626
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Cheung, C., Remmen, G.N. Hidden simplicity of the gravity action. J. High Energ. Phys. 2017, 2 (2017). https://doi.org/10.1007/JHEP09(2017)002
- Classical Theories of Gravity
- Scattering Amplitudes
- Effective Field Theories