Finiteness of 3D higher spin gravity Landscape

We give Swampland constraints on the three dimensional Landscape of Anti-de Sitter higher spin gravity in the Chern–Simons formulation with connection valued in various split real forms of Lie algebras. We derive the finiteness conjecture by computing the upper bound on the rank of possible gauge groups then we refine it using the AdS distance conjecture. We discuss the implications of this Swampland 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.