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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  

Preprint Link:  https://arxiv.org/abs/2406.09151v1 (pdf) 
Date submitted:  20240726 16:36 
Submitted by:  Sammani, Rajae 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 (s1\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 ( s1 \right ) +[1 \left ( \mu l_{AdS_{3}} \right ) ^{2} \left ( s1 \right ) ]$.
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 Provide a novel and synergetic link between different research areas.
 Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work
 Detail a groundbreaking theoretical/experimental/computational discovery
 Present a breakthrough on a previouslyidentified and longstanding research stumbling block
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Report
The authors conjecture a possible extension of the Weak Gravity Conjecture (WGC) to higher spin massive topological gravity on AdS3 backgrounds by considering the decay of the higher spin generalization of BTZ black holes in these theories. To develop their conjecture, they need to identify the appropriate states that conjecturally mediate the discharge of these black holes, and discuss their mass, charge, and coupling. They argue for this identification by using a ChernSimons formulation of higherspin AdS3 gravity, supplemented by a mass term.
The questions studied in this paper are relevant for extending the applicability of one of the most consequential and wellstudied conjectures in the swampland program, and are thus a valuable addition to the swampland literature.
Before recommending the paper for publication, I would like to ask a few clarification questions to the authors:
1. Could the authors provide a short selfcontained review of the massive formulation the higherspin theory? Specifically, it would be beneficial for the reader if the authors could review the properties of the action (4.3) and, in particular, how formula (4.4) is obtained. This is particularly relevant in light of the fact that (4.4) is the crucial starting point for their derivation of the inequalities in section 4.1.
2. It would also beneficial if the authors could expand their discussion in section 5 by commenting on the differences between the topological nature of the theory they are considering, with local degrees of freedom added by the mass deformation, with the more standard setup of the WGC with local U(1) degrees of freedom.
3. The authors mention in the introduction that for AdS3 weak forms of the WGC are not enough to ensure black hole decay, thus requiring a lattice version of the WGC. Is it obvious that this same argument directly applies to the higherspin case? Could it be that the selfinteracting particle condensates might not form in the class of theories the authors are considering? It can be helpful for the readers if the authors could expand on this point, discussing possible difference that might arise in higherspin theories.
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Ask for minor revision