Cheung, Clifford (2012) Gravity amplitudes from nspace. Journal of High Energy Physics, 2012 (12). Art. No. 057. ISSN 11266708. http://resolver.caltech.edu/CaltechAUTHORS:20130325145830606

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Abstract
We identify a hidden GL(n,ℂ) symmetry of the tree level npoint MHV gravity amplitude. Representations of this symmetry reside in an auxiliary nspace whose indices are external particle labels. Spinor helicity variables transform nonlinearly 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 3planes in nspace. 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  

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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 DEAC0205CH11231, and by the National Science Foundation under grant PHY0855653. C.C. is indebted to Nima ArkaniHamed for a timely reminder of C.C's earlier unpublished note from 2009 relating MHV amplitudes to the matrix tree theorem.  
Group:  Caltech Theory  
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Subject Keywords:  Scattering Amplitudes; Classical Theories of Gravity  
Record Number:  CaltechAUTHORS:20130325145830606  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20130325145830606  
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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