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Kaluza-Klein spectrometry for ${\rm AdS_{3}}$ vacua
by Camille Eloy
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Submission summary
| Authors (as registered SciPost users): | Camille Eloy |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2011.11658v1 (pdf) |
| Date submitted: | 2020-12-01 11:39 |
| Submitted by: | Eloy, Camille |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We use exceptional field theory to compute Kaluza-Klein mass spectra around ${\rm AdS_{3}}$ vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of ${\cal N}=(2,0)$ and ${\cal N}=(1,1)$ six-dimensional supergravities on ${\rm AdS_{3}}\times S^{3}$ and of type II supergravity on ${\rm AdS_{3}}\times S^{3}\times S^{3}\times S^{1}$.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2021-4-22 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2011.11658v1, delivered 2021-04-22, doi: 10.21468/SciPost.Report.2823
Strengths
1. Clear presentation throughout, with self contained summary of relevant background at the beginning of the paper.
2. Results are technically sound and important in the context of both the AdS/CFT correspondence and in applications of exceptional field theory.
Weaknesses
No significant weaknesses
Report
This paper concerns the computation of the Kaluza-Klein spectrum for AdS3 vacua, using the more efficient methodology from exceptional field theory rather than explicit harmonic analysis. The paper builds on a number of works by the Lyon group and does not introduce particularly new techniques. Nonetheless the results obtained in this work are important in the context of holographic correspondences and also in exploring how the exceptional field theory programme can be developed. The most interesting analysis in this work relates to the case in which group theory alone does not fix the spectrum i.e. the AdS3 x S3 x S3 x S1 background, a duality that has been very fruitful for study over many years. The paper is very clearly written and presented and could be published with no changes.
Report #1 by Anonymous (Referee 2) on 2020-12-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2011.11658v1, delivered 2020-12-28, doi: 10.21468/SciPost.Report.2341
Report
This paper formulates a very effective technique to compute the mass spectra of Kaluza-Klein fluctuations around certain classes of supergravity solutions by exploiting a reformulation of half-maximal supergravities in terms of $D=3$ extended field theory based on an O$(8,n)$ duality group.
These solutions are products of an "external" AdS$_3$/Minkoswski$_3$/dS$_3$ factor with an internal generalised parallelisable space (which gives rise to a so-called generalised Scherk-Schwarz reduction to a $D=3$ gauged supergravity).
This class of solutions includes some known and previously studied AdS$_3$ solutions which the author uses to exemplify the effectiveness of the formalism.
This whole approach is a generalisation of the results in 1911.12640 and 2009.03347, which apply to backgrounds with an "external" factor of dimension $D\ge4$.
There are subtleties inherent in the extended generalised geometry for the $D=3$ case as well as in the structure of the equations of motion that make the analysis in this paper a non-trivial generalisation of the previous literature and certainly worth the effort, given how it greatly simplifies the study of certain Kaluza--Klein spectra.
The paper is well written and detailed and will certainly provide a basis for future studies of mass spectra for much larger classes of AdS$_3$ supergravity solutions in the future, and their application to AdS/CFT and to the swampland program. I believe the following point needs to be addressed before publication:
1) The Ansatz for the Kaluza-Klein fluctuations of the constrained vector fields $\mathcal{B}_{\mu\,MN}$ in equation (3.2) should be motivated explicitly, given that these fields are one of the main differences between $D=3$ and higher-$D$ extended field theories. I can see how the expression provided is the natural generalisation of the generalised Scherk-Schwarz Ansatz (2.13), and that such natural generalisation works for the other fields. However, the Ansatz for $\mathcal{B}_{\mu\,MN}$ cannot be directly deduced from the expressions in 2009.03347 (I would imagine deducing it from an Ansatz for the constrained two-forms in $D=4$, but this is not explcit there either). In particular, it should be explained why it is acceptable that their fluctuations are not independent from those of the standard vector fields. Were the equations of motion used to derive this result? Is the last line of (3.2) only motivated "a posteriori" by consistency of the linearised equations of motion and explicit results in later sections?
Also, the following points are very minor but worth pointing out
2) At the beginning of the Introduction the author refers to past literature on KK spectroscopy on coset spaces. The sentence gives the impression that the techniques derived here apply for more general manifolds, but in fact globally generalsed parallelisable spaces are known to always be (topologically) homogeneous (see 0807.4527 section 5.3).
3) Related to the previous point, it seems to me that the $\rm G_{max}$ group introduced around equation (3.3) is really the group that has a transitive action on the coset space, or perhaps its compact subgroup? I would suggest to clarify this point in view of future applications.