Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

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.

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

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Cited by in corpus (9)

• An Introduction to On-shell Recursion Relations
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Gravitons, Bose-symmetry, and Bonus-scaling
• Note on Permutation Sum of Color-ordered Gluon Amplitudes
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Bonus scaling and BCFW in N=7 supergravity
• Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes