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Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

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He,  Song
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1011.4287
(Preprint), 626KB

JHEP02_2011_005.pdf
(Any fulltext), 587KB

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Citation

He, S., Nandan, D., & Wen, C. (2011). Note on Bonus Relations for N=8 Supergravity Tree Amplitudes. Journal of high energy physics: JHEP, 2011(2): 005. doi:10.1007/JHEP02(2011)005.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-D195-1
Abstract
We study the application of non-trivial relations between gravity tree amplitudes, the bonus relations, to all tree-level amplitudes in N=8 supergravity. We show that the relations can be used to simplify explicit formulae of supergravity tree amplitudes, by reducing the known form as a sum of (n-2)! permutations obtained by solving on-shell recursion relations, to a new form as a (n-3)!-permutation sum. We demonstrate the simplification by explicit calculations of the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (N^2MHV) amplitudes, and provide a general pattern of bonus coefficients for all tree-level amplitudes.