Swampland constraints on higher spin AdS$_{3}$ gravity Landscape

We give Swampland constraints for the three dimensional Landscape of Anti-de Sitter gravity in the Chern-Simons formulation with connection valued in various split real forms of Lie algebras. We derive explicitly the limit on the number of massless modes by computing the upper bound on the rank of possible gauge groups and thus validating this Swampland conjecture in 3D. We discuss the implications of this constraint on the spectrum of higher spin gravity theories and we compare it with the gravitational exclusion principle required from BTZ black hole consideration to excerpt a constraint on the Chern-Simons level k.
Comment: LaTeX, 43 pages, 8 Figures