Abstract
We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.
Highlights
The ultraviolet behavior of gravity scattering amplitudes has been of great interest for several decades [1,2,3,4,5,6]
One well-known mechanism to improve and tame the UV behavior of a theory is to introduce supersymmetry which enforces certain cancelations of divergences in loop diagrams due to superpartners running in the loop
This famously leads to the cancelation of quadratic corrections to the Higgs mass but naively it can not solve the problem in gravity where power-counting would eventually win over any amount of supersymmetry
Summary
The ultraviolet behavior of gravity scattering amplitudes has been of great interest for several decades [1,2,3,4,5,6]. This famously leads to the cancelation of quadratic corrections to the Higgs mass but naively it can not solve the problem in gravity where power-counting would eventually win over any amount of supersymmetry This expectation is related to the standard picture where UV divergences of scattering amplitudes are closely linked to the appearance of counterterms which satisfy all symmetry requirements of a given theory. It has been known for a while that graviton tree-level amplitudes have a surprisingly tame large z behavior for BCFW shifts [50,51,52] despite the naive power-counting expectations This feature of gravity trees has been linked to improved UV properties of one-loop amplitudes in e.g.
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