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Gravity loop integrands from the ultraviolet
by Alex Edison, Enrico Herrmann, Julio Parra-Martinez, Jaroslav Trnka
- Published as SciPost Phys. 10, 016 (2021)
|As Contributors:||Julio Parra-Martinez|
|Date submitted:||2020-11-23 19:25|
|Submitted by:||Parra-Martinez, Julio|
|Submitted to:||SciPost Physics|
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.
Published as SciPost Phys. 10, 016 (2021)
Author comments upon resubmission
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.
Submission & Refereeing History
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