Finiteness of 3D higher spin gravity Landscape

TL;DR

This paper establishes Swampland constraints on 3D higher spin gravity in AdS, deriving finiteness conditions on gauge groups and levels, impacting the spectrum and consistency of these theories.

Contribution

It introduces a finiteness conjecture for 3D higher spin gravity based on gauge group bounds and refines it with the AdS distance conjecture, linking Swampland criteria to higher spin spectra.

Findings

Upper bound on gauge group rank derived

Refined finiteness conjecture using AdS distance conjecture

Constraint on Chern-Simons level k from black hole considerations

Abstract

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.