# Reconstructing the graviton

### Submission summary

 As Contributors: Manuel Reichert Arxiv Link: https://arxiv.org/abs/2102.02217v2 (pdf) Date submitted: 2021-07-29 16:32 Submitted by: Reichert, Manuel Submitted to: SciPost Physics Academic field: Physics Specialties: Gravitation, Cosmology and Astroparticle Physics High-Energy Physics - Theory Approach: Theoretical

### Abstract

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2102.02217v3 on 7 October 2021

Resubmission 2102.02217v2 on 29 July 2021
Submission 2102.02217v1 on 17 February 2021

## Reports on this Submission

### Anonymous Report 2 on 2021-8-25 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2102.02217v2, delivered 2021-08-25, doi: 10.21468/SciPost.Report.3441

### Report

Though the authors said that they tried to improve the presentation in sect. 5, I do not see much change. However, there are several other places that they improved. The fact that the spectral function is the object that is important, is emphasized. About the second point I made, the author gave additional explanation and this is fine. There are several errors in the manuscript, like reference to Sec.IV C above eq.(55) which is inside Sec.IV C itself, and I suppose they mean that Sec.IV A. I recommend the authors to take another careful check to remove this kind of minor mistakes. After that, I think that this paper may be published.

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### Author:  Manuel Reichert  on 2021-10-06  [id 1815]

(in reply to Report 2 on 2021-08-25)

We thank the referee for pointing out the reference error, which we have corrected. We carefully checked the manuscript for further minor mistakes.

### Anonymous Report 1 on 2021-8-9 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2102.02217v2, delivered 2021-08-09, doi: 10.21468/SciPost.Report.3359

### Report

The authors have answered all my concerns satisfactorily. There is however one new concern that I would like to bring forward. Comparing to the first version, the reconstruction of the background spectral function seems to have changed in the new version, but no changes have been indicated in the authors' reply/comments on resubmission. This in particular concerns the prefactor of the logarithm/the hypergeometric function ($A_{\bar g}$) related to the parameterisation of the propagator, but also the qualitative behaviour of the spectral function itself. I noticed that the fit parameters $\Delta\Gamma_{1,2}$ have changed from 2 to 5, but the authors write that their values have no impact on the reconstruction. Table II has also changed considerably. The background propagator itself shows no noticeable difference. The authors should explain what has happened here, and how this is in agreement with the error estimates for the reconstructed spectral function.

If the above concern is addressed adequately, I would be happy to recommend the paper for publication.

As a final minor point, following up on the question of numerically accessible Lorentzian formulations, it seems that there are some new developments in the field of spin foams, see [2104.00485]. I leave it to the authors whether they want to include a reference to this.

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### Author:  Manuel Reichert  on 2021-08-23  [id 1699]

(in reply to Report 1 on 2021-08-09)

We apologise for the confusion regarding the computation of the background spectral function. In the previous version of this work, we had treated the low momentum dependence only numerically, which lead to an oversight of a contribution to the log-like divergence. In the present version, we computed the log-like IR contributions analytically (c.f. the computation of $A_{\bar g}$), which allowed us to improve the numerics in the IR. This has resulted in a slightly simpler background spectral function (a smaller number of Breit-Wigner structures in Table 2) and a smaller error in the reconstruction ($E_\text{rel} < 10^{-3}$ vs $E_\text{rel} < 10^{-2}$ before). The only remarkable change in the background spectral function is that it now starts negative in the deep IR, otherwise all features remained qualitatively the same. The different choice of parameters $\Delta\Gamma_{1,2}$ has no impact on the reconstruction.

We hope that this clears up the referee's concern. We also thank the referee for bringing the reference to our attention, which we will cite in the next version of our work.