N=8 Supergravity 4-point Amplitudes

Abstract

We present the explicit expressions in N=8 supergravity for the bosonic 4-particle tree and 1-loop amplitudes including vectors and scalars. We also present the candidate 4-point UV divergences in a form of helicity amplitudes, corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on a conjectured higher loop finiteness. We perform a supersymmetric deformation to complex momentum of the 4-point generating function including higher-loop counterterms and the 1-loop UV finite amplitudes. Using the explicit form of the scalar part of the 3-loop counterterm and of the 1-loop UV finite scalar 4-point amplitudes we find that they both have an unbroken E7 symmetry. We derive from E7 symmetry the low-energy theorem for the 1-loop n-point amplitudes.

23 p, 4 figures

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• A simple approach to counterterms in N=8 supergravity
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• E{7(7)} Symmetry and Finiteness of N=8 Supergravity
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Tree-Level Amplitudes in N=8 Supergravity
• Unraveling L_{n,k}: Grassmannian Kinematics
• E7(7) invariant Lagrangian of d=4 N=8 supergravity
• N=8 Supergravity on the Light Cone
• SUSY Ward identities, Superamplitudes, and Counterterms
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• The Ultraviolet Finiteness of N=8 Supergravity
• New E77 invariants and amplitudes
• The D^{2k} R^4 Invariants of N=8 Supergravity
• Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
• Duality Constraints on Counterterms in $\mathcal{N}=5,6$ Supergravities
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry
• An Update on Perturbative N=8 Supergravity
• Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity
• Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace