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Gravity loop integrands from the ultraviolet
by Alex Edison, Enrico Herrmann, Julio Parra-Martinez, Jaroslav Trnka
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Submission summary
| Authors (as registered SciPost users): | Julio Parra-Martinez |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202008_00003v1 (pdf) |
| Date submitted: | 2020-08-04 00:14 |
| Submitted by: | Parra-Martinez, Julio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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Abstract
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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-10-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202008_00003v1, delivered 2020-10-15, doi: 10.21468/SciPost.Report.2084
Report
The manuscript "Gravity loop integrands from the ultraviolet" studies the
behaviour of the integrand of $\mathcal{N} = 8$ loop amplitudes at large momentum.
There are three technical points, which are of interest to the community.
The new results of the authors are:
(i) four-dimensional unitarity cuts have a better ultraviolet behaviour than expected.
(ii) a reconstruction of the loop integrand from the improved ultraviolet scaling and the vanishing
at particular points in momentum space
(iii) the discussion of new multi-line shifts for BCFW-type recursion relations.
These results, albeit technical in nature, are helpful for the community and worth publishing.
The driving force behind these results is the desire of the authors to understand the "raison d'etre"
for the improved ultraviolet behaviour.
The authors openly admit in their manuscript that so far they have not found a good explanation.
At various places the authors hint at speculations, without giving sufficient information to the readers.
This makes it difficult for the readers to understand what the authors have in mind.
It would not degrade the manuscript, if these passages are left out.
There are a few smaller points, where clarifications could be helpful:
Page 6: "minimal power counting of an integral": The authors could define this term.
The authors could also elaborate why the maximal cuts determine this, the readers might get lost at this point otherwise.
Page 27, section 4.3: " ... it shows that the $\mathcal{N} = 8$ supergravity loop integrand can be fully fixed
using only homogeneous constraints at infinity."
In general or just for the examples discussed above?
Page 31, two lines after eq.(5.5): Does "term 1" refer to the first term in eq.(5.5) or to eq.(5.3)?
Report #1 by Anonymous (Referee 1) on 2020-10-11 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202008_00003v1, delivered 2020-10-11, doi: 10.21468/SciPost.Report.2069
Strengths
1- Very clear discussion of the results
2- Paper gives important insight into the structure of gravity amplitudes
Weaknesses
none
Report
The paper discusses UV properties of gravity amplitudes, both in pure gravity and and supersymmetric theories. It proposes an unexpected scaling behaviour of the amplitudes for large loop momenta in 4 dimensions (which is absent for YM). Understanding the UV properties of gravity amplitudes in 4 dimensions is important in order to uncover possible cancellations which may lead to an improved UV behaviour of gravity amplitudes. This in turn may lead to new ways to prove, or disprove, the UV finiteness of N=8 SUGRA in 4 dimensions. The paper proposes an interesting new direction to understand the UV structure of 4-dimensional gravity theories.
The paper is well written, and the results are clearly presented and discussed. I recommend the paper for publication, but I suggest that the authors address the points raised below.
Requested changes
1- At the very bottom of page 13, the authors say that they "get e.g. $t^4$ for GR and $1/t^{L−2}$ for YM". While I can see the $1/t^{L−2}$ scaling in Figure 2, I seem to see a scaling of $t^3$ for GR. Is this a typo? The authors should clarify this point.
2- Figure 2 could benefit from having also the scaling of the $D$-dimensional amplitudes on the same plot (e.g., as a thin line). This would convey more clearly the message of the difference between the 4- and $D$-dimensional cases.