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Radiative Asymptotic Symmetries of 3D EinsteinMaxwell Theory
by Jorrit Bosma, Marc Geiller, Sucheta Majumdar, Blagoje Oblak
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Submission summary
Authors (as registered SciPost users):  Marc Geiller · Blagoje Oblak 
Submission information  

Preprint Link:  scipost_202311_00051v1 (pdf) 
Date submitted:  20231130 13:58 
Submitted by:  Oblak, Blagoje 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study the null asymptotic structure of EinsteinMaxwell theory in threedimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate electromagnetic radiation. We derive falloff conditions for the Maxwell field that contain both Coulombic and radiative modes with nonvanishing news. The latter produces nonintegrability and fluxes in the asymptotic surface charges, and gives rise to a nontrivial 3D Bondi mass loss formula. The resulting solution space is thus analogous to a dimensional reduction of 4D pure gravity, with the role of gravitational radiation played by its electromagnetic cousin. We use this simplified setup to investigate choices of charge brackets in detail, and compute in particular the recently introduced Koszul bracket. When the latter is applied to WaldZoupas charges, which are conserved in the absence of news, it leads to the fielddependent central extension found earlier in [Barnich, Lambert, Mao, 1503.00856]. We also consider (Anti)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024216 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202311_00051v1, delivered 20240216, doi: 10.21468/SciPost.Report.8571
Strengths
1  Presentation and complete study of a concrete nontrivial radiative system in threedimensional gravity with matter that mimics crucial features of fourdimensional radiative gravitational phase space.
2  Comprehensive, detailed and interesting discussion of the various proposals for modified brackets for algebras of nonintegrable charges.
3  Provides a good technical background for future analyses in flat space holography and a formulation of celestial amplitudes in three dimensions.
4  The quality of the writing and the clarity of the presentation make the reading really enjoyable and enriching.
Weaknesses
None
Report
This paper studies the asymptotic dynamics of threedimensional Einstein gravity coupled to a Maxwell field, for both vanishing and nonvanishing values of the cosmological constant. Since the electromagnetic field describes a propagating degree of freedom in three dimensions, the combination of the two theories provides a nice toy model for radiative spacetimes in fourdimensional Einstein gravity, which has the good taste of being technically more tractable, but from which one can still draw important conclusions than can be applied to the more complicated higherdimensional case.
For example, it is shown that the asymptotic charges are not conserved in (retarded) time, since EinsteinMaxwell dynamics prescribes fluxbalance laws instead of conservation laws due to the electrodynamic radiative degree of freedom, which mimic the celebrated Bondi mass and angular momentum fluxbalance equations in four dimensions. Moreover, due to the coupling with radiative fields, the asymptotic charges are found to be nonintegrable. Since this nonintegrability is essential in the presence of radiation, \textit{i.e.} it cannot be completely removed by a fielddependent transformation of the gauge parameters, several proposals for modified charge brackets have emerged, from the seminal work of Barnich and Troessaert to more recent approaches (\textit{e.g.} ref. [98]).
One of the key points of the paper is the application of the different proposals to the concrete and technically less complicated system presented above and the associated critical description of the virtues and the drawbacks of each definition, which is very interesting. This can shed new light on previous analyses of covariant phase space descriptions of radiative gravitational systems, and teach us much for future endeavours, namely on how to construct an ``ultimate'' version of the modified charge bracket that could consistently lift the standard Peierls/Dirac bracket to systems with nonconservative boundary conditions, hence nonconserved/nonintegrable asymptotic charges.
The paper is very well written, the motivations are always clear and detailed, and the Authors have taken particular care to write the mathematical derivations in such a way that one can easily and fluently jump from one step to another. The results are scientifically sound and timely, considering the growing interest in flat space holography in the HEP community, for which one needs to understand how to encode Bondi fluxbalance laws from an intrinsic boundary perspective. As it discusses a theory with nontrivial electrodynamic bulk scattering from the point of view of null infinity, this paper could also be considered as a first step towards the formulation of celestial amplitudes in three dimensions, where the ``holographic screen'' is no longer the null plane at infinity, but the onedimensional celestial circle. In conclusion, I am happy to recommend this paper for publication in SciPost for the quality of the presentation, the relevance of the results to current research, and for the numerous avenues it can open for future investigations.
Requested changes
None
Report #1 by Anonymous (Referee 1) on 2024211 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202311_00051v1, delivered 20240211, doi: 10.21468/SciPost.Report.8540
Strengths
1Provides the first discussion of "news" in a 2+1 dimensional context
2EinsteinMaxwell gravity in 3d hence provides a simple toy model that overcomes issues with other 3d toy models (radiation to scri, news, mass loss formula, etc.)
3Authoritative discussion of asymptotic symmetries and associated algebras with high level of precision and generality
Weaknesses
1Model does not allow for black holes in absence of cosmological constant and hence has limited scope
Report
I was impressed when reading this paper. While one could say "this could have been done in the 1990ies" it is a fact that it wasn't, and it takes both courage and endurance to embark on such an adventure. In my opinion, the authors did a great job at all levels: in the abstract and introduction, they made the case so clear that even outsiders to the field should be able to appreciate what this paper does, why it does it, and why the results are relevant for physics and of technical interest. In the body of the paper, the technical results are presented in sufficient detail to allow students and experts to follow the key developments while avoiding being too verbose. The language used is very clear and unpretentious. My only (minor) qualm is with section 6, which appears like an afterthought (and perhaps that is what it really is, and it is ok). I am sure that more could be said about (A)dSEinsteinMaxwell in 3d, but I am fine with the authors' choice not to elaborate further on this story in the present paper. The outlook section 7 is also useful and enjoyable to read. However, from my perspective,there is a glaring omission: the authors do not mention a possible supersymmetric extension, which seems slightly odd.
I am happy to recommend the paper for publication in SciPost Phys., either in its present form or with the suggested inclusion on SUSY (see below), without further review.
Requested changes
I wouldn't say I request this change, but I strongly encourage the authors to add in the outlook section 7 another item in their itemized list addressing prospects of generalizing their analysis to supersymmetric (AdS)MaxwellEinstein in 3d.