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Higher spin swampland conjecture for massive AdS$_{3}$ gravity
by R. Sammani, E. H Saidi
Submission summary
| Authors (as registered SciPost users): | Rajae Sammani |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2406.09151v2 (pdf) |
| Date submitted: | 2024-12-16 15:14 |
| Submitted by: | Sammani, Rajae |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper, we show that a possible version of the swampland weak gravity conjecture for higher spin (HS) massive topological AdS$_{3}$ gravity can be expressed in terms of mass $M_{hs}$, charge $Q_{hs}$ and coupling constant $g_{hs}$ of 3D gravity coupled to higher spin fields as $M_{hs} \leq \sqrt{2}$ $Q_{hs}$ $g_{hs}$ $M_{Pl}$. The higher spin charge is given by the $SO(1,2)$ quadratic Casimir $Q_{hs}^{2}=s\left (s-1\right) $ and the HS coupling constant by ${\large g}_{hs} ^{2}=2/\left (M_{Pl}^{2} l_{AdS_{3}}^{2}\right )$ while the mass expressed like $\left( l_{AdS_{3}} \text{M}_{hs}\right) ^{2}$ is defined as $ \left (1+\mu l_{AdS_{3}} \right ) ^{2} s \left ( s-1 \right ) +[1- \left ( \mu l_{AdS_{3}} \right ) ^{2} \left ( s-1 \right ) ]$.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1- addressed almost all points raised by referees
Weaknesses
1- one crucial point remains a little weak
Report
In this new version, the authors did add a review about (4.4), as also asked by the other referee.
Below (4.23), the authors also tried addressing my other question, about why $s(s-1)$ can be interpreted as a charge. I thank them for their effort. But I have to confess that I am not sure I follow the logic here: in the last line of p. 16, "an extremal higher spin BTZ black hole is then a black hole with mass equal to $M_{\rm hs}^2 = \left(\frac1{l_{\rm AdS_3}}+\mu \right)^2 j(j+1)$", where does this formula come from? Is this a circular argument?
I think the idea is roughly speaking to compare the extremality bound for Kerr–Newman to the expected WGC bound; for them to coincide, the $a^2$ term has somehow to coincide with $Q^2$.
My response to this is that $a$ here is the _angular momentum_ of the black hole, not quite the spin of the particles in the theory. I can see that probably the extremal Kerr–Newman in the higher spin theory might be similar to this one. But I think it might be possible to make this a lot sharper by comparing with existing literature. There is for example 1404.3305 (see for example the comment below (3.40) there), but a lot more has probably been done since then.
So as a final request I would urge the authors to rewrite the part below (4.23) a little more clearly, and to try to look whether this feature persists in actual higher spin theories. If this is hard, I would ask them to justify why.
Recommendation
Ask for minor revision