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Gravity loop integrands from the ultraviolet

by Alex Edison, Enrico Herrmann, Julio Parra-Martinez, Jaroslav Trnka

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Julio Parra-Martinez
Submission information
Preprint Link: scipost_202008_00003v2  (pdf)
Date accepted: 2021-01-21
Date submitted: 2020-11-23 19:25
Submitted by: Parra-Martinez, Julio
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory


We demonstrate that loop integrands of (super-)gravity scattering ampli- tudes 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 com- pared 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 homoge- neous. 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.

Author comments upon resubmission

We thank the referees for useful suggestions that have improved the general presentation of the paper.
We believe these changes address all the points raised by the referees and hope these improvements are sufficient to allow publication.

List of changes

We have implemented the following changes:

1. The typographical error in the scaling for general relativity at the bottom of page 13 pointed out in Report 1 has been corrected.
2. Thin lines have been added to Figure 2 explaining the scaling of D-dimensional unitarity cuts.
3. Footnote 6 now contains a definition of “minimal power-counting”.
4. A parenthetical remark has been added in section 4.3 clarifying which integrands in N=8 can be fixed via homogeneous constraints.
5. Eq. (5.3) has been modified to clarify references in the text to “term 1” and “term 2”.
6. The more speculative comments about the implications of the results of this work have been removed from the main text and adapted for the conclusions.

Published as SciPost Phys. 10, 016 (2021)

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