Higher spin swampland conjecture for massive AdS${}_3$ gravity

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 $M_{hs}\le \sqrt{2}$ $Q_{hs}$ $g_{hs}$ $M_{Pl}$. 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 $g_{hs}^2=2/\left(M_{Pl}^2{l}_{Ad{S}_3}^2\right)$ while the mass expressed like ${\left(l_{Ad{S}_3}{\text{M}}_{hs}\right)}^2$ is defined as ${\left(1+\hat{I}¼l_{Ad{S}_3}\right)}^{2}s\left(s-1\right)+[1-{\left(\hat{I}¼l_{Ad{S}_3}\right)}^2\left(s-1\right)]$.