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Twofold Symmetries of the Pure Gravity Action

Cheung, Clifford and Remmen, Grant N. (2017) Twofold Symmetries of the Pure Gravity Action. Journal of High Energy Physics, 2017 (01). Art. No. 104. ISSN 1126-6708. doi:10.1007/JHEP01(2017)104.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Remmen, Grant N.0000-0001-6569-8866
Additional Information:© 2017 The Author(s). This article is distributed under the terms of the Creative Commons, Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: 18 December 2016; Accepted: 02 January 2017; First Online: 25 January 2017. We thank Nima Arkani-Hamed, Zvi Bern, Sean Carroll, Roberto Percacci, Alan Weinstein and Mark Wise for useful discussions and comments. C.C. is supported by a Sloan Research Fellowship and a DOE Early Career Award under Grant No. DE-SC0010255. G.N.R. is supported by a Hertz Graduate Fellowship and a NSF Graduate Research Fellowship under Grant No. DGE-1144469.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0010255
Fannie and John Hertz FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144469
Subject Keywords:Classical Theories of Gravity; Field Theories in Higher Dimensions; Scattering Amplitudes
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Issue or Number:01
Record Number:CaltechAUTHORS:20161214-085951208
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Official Citation:Cheung, C. & Remmen, G.N. J. High Energ. Phys. (2017) 2017: 104. doi:10.1007/JHEP01(2017)104
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72803
Deposited By: Joy Painter
Deposited On:14 Dec 2016 17:09
Last Modified:11 Nov 2021 05:06

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