Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

Details Note on Bonus Relations for N=8 Supergravity Tree Amplitudes Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

2010-11-18

arxiv.org/abs/1011.4287v2

JHEP 1102:005,2011

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 9 figures; v2, minor changes, references added

Scientific paper

10.1007/JHEP02(2011)005

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.

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