Twofold symmetries of the pure gravity action

Cheung, Clifford; Remmen, Grant N.

doi:10.1007/JHEP01(2017)104

Twofold symmetries of the pure gravity action

Journal Article · Tue Jan 24 23:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP01(2017)104· OSTI ID:1360789

Cheung, Clifford ^[1]; Remmen, Grant N. ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; DOE/OSTI
California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Here, 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. Finally, 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.

View Accepted Manuscript (DOE)

Research Organization:: California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: SC0010255

OSTI ID:: 1360789

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2017; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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The double copy: gravity from gluons White, Chris D. arXiv https://doi.org/10.48550/arxiv.1708.07056	text	January 2017
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Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings Vines, Justin arXiv https://doi.org/10.48550/arxiv.1709.06016	text	January 2017
The Kerr-Schild double copy in curved spacetime Bahjat-Abbas, Nadia; Luna, Andrés; White, Chris D. arXiv https://doi.org/10.48550/arxiv.1710.01953	text	January 2017
Soft collinear effective theory for gravity Okui, Takemichi; Yunesi, Arash arXiv https://doi.org/10.48550/arxiv.1710.07685	text	January 2017
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Gravitational radiation from the classical spinning double copy Li, Jingping; Prabhu, Siddharth G. arXiv https://doi.org/10.48550/arxiv.1803.02405	text	January 2018
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