Celestial Holography: Lectures on Asymptotic Symmetries

Submission summary

 As Contributors: Geoffrey Compère Preprint link: scipost_202109_00027v1 Date submitted: 2021-09-21 21:14 Submitted by: Compère, Geoffrey Submitted to: SciPost Physics Lecture Notes Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

Abstract

The aim of these Lectures is to provide a brief overview of the subject of asymptotic symmetries of gauge and gravity theories in asymptotically flat spacetimes as background material for celestial holography.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission scipost_202109_00027v1 on 21 September 2021

Reports on this Submission

Report

This is a review on the subject of asymptotic symmetries, a theme of active research. It covers basic aspects of the general formulation of the problem and discusses in some detail a few important instances, including structure and significance of the BMS group in three and four dimensions.

The presentation is clear, although coincise, and may provide a good starting point for researchers interested in approaching the subject. The material is presented from an up-to-date perspective taking recent advances into account, e.g. the definition of ASG as including the asymptotic symmetries of all possible dual formulation of a theory or the role of subleading symmetries in accounting for memory effects.

I recommend publication in the present journal.

Requested changes

I spotted a few typos:

1. Eq (15) and four lines below: \phi_+ and \phi_- should probably carry additional labels (compare with previous page)
2. Below eq (28): with insight'' --> with hindsight'' (I guess)
3. Page 10, sentence starting at line 3; it seems a few words are missing:  The central [charge] has therefore dimension[s of] inverse length''
4. Page 10, line 4 Poincare --> Poincaré
5. Page 11, line 2: path --> past
6. Page 11, beginning of section 2.3: the first sentences doesn't sound correct; maybe enough to change the first is'' into to''
7. Page 13, below eq (52): dotes --> dots
8. Page 14, below eq (57): `where M(\theta, \phi) [...]'' sounds like the quantity M was introduced in the previous equations.

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Report

The Lectures cover the topic of asymptotic symmetries in gravity and gauge theories, and are aimed in particular at readers interested in celestial holography, which is a very timely topic. The review is very interesting and covers a large number of tpics - because of this it is not necessarily entirely self-contained - however the authors have clearly referenced the sources where the additional details can be found.

I recommend publication.
I only have a number of very small comments that could help with clarity:
- at the top of page 4, mention that n is the space-time dimension
- in eqn. 15, I think the phi's are missing superscripts
- in the paragraph ebove eqn (37), one of the r's should be t

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -