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Gravity amplitudes from n-space

Cheung, Clifford (2012) Gravity amplitudes from n-space. Journal of High Energy Physics, 2012 (12). Art. No. 057. ISSN 1126-6708. http://resolver.caltech.edu/CaltechAUTHORS:20130325-145830606

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Abstract

We identify a hidden GL(n,ℂ) symmetry of the tree level n-point MHV gravity amplitude. Representations of this symmetry reside in an auxiliary n-space whose indices are external particle labels. Spinor helicity variables transform non-linearly under GL(n,ℂ), but linearly under its notable subgroups, the little group and the permutation group S_n. Using GL(n,ℂ) covariant variables, we present a new and simple formula for the MHV amplitude which can be derived solely from geometric constraints. This expression carries a huge intrinsic redundancy which can be parameterized by a pair of reference 3-planes in n-space. Fixing this redundancy in a particular way, we reproduce the S_(n−3) symmetric form of the MHV amplitude of [1], which is in turn equivalent to the S_(n−2) symmetric form of [2] as a consequence of the matrix tree theorem. The redundancy of the amplitude can also be fixed in a way that fully preserves S_n, yielding new and manifestly S_n symmetric forms of the MHV amplitude. Remarkably, these expressions need not be manifestly homogenous in spinorial weight or mass dimension. We comment on possible extensions to N^(k−2)MHV amplitudes and speculate on the deeper origins of GL(n,ℂ).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/JHEP12(2012)057DOIArticle
http://link.springer.com/article/10.1007%2FJHEP12%282012%29057PublisherArticle
http://arxiv.org/abs/1207.4458arXivDiscussion Paper
Additional Information:© 2012 SISSA. Published for SISSA by Springer. Received: September 3, 2012; Accepted: November 24, 2012; Published: December 12, 2012. C. C. is supported by the Director, Office of Science, Office of High Energy and Nuclear Physics, of the US Department of Energy under Contract DE-AC02-05CH11231, and by the National Science Foundation under grant PHY-0855653. C.C. is indebted to Nima Arkani-Hamed for a timely reminder of C.C's earlier unpublished note from 2009 relating MHV amplitudes to the matrix tree theorem.
Group:Caltech Theory
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-05CH11231
NSFPHY-0855653
Subject Keywords:Scattering Amplitudes; Classical Theories of Gravity
Record Number:CaltechAUTHORS:20130325-145830606
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130325-145830606
Official Citation:Cheung, C. J. High Energ. Phys. (2012) 2012: 57. doi:10.1007/JHEP12(2012)057
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37615
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Apr 2013 23:12
Last Modified:23 Mar 2017 22:01

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