Critical solutions of topologically gauged $ \mathcal{N} $ = 8 CFTs in three dimensions

A bstractIn this paper we discuss some special (critical) background solutions that arise in topological gauged $ \mathcal{N} $ = 8 three-dimensional CFTs with SO(N) gauge group. Depending on how many scalar fields are given a VEV the theory has background solutions for certain values of μl, where μ and l are parameters in the TMG Lagrangian. Apart from Minkowski, chiral round AdS3 and null-warped AdS3 (or Schrödinger(z = 2)) we identify also a more exotic solution recently found in TMG by Ertl, Grumiller and Johansson. We also discuss the spectrum, symmetry breaking pattern and the supermultiplet structure in the various backgrounds and argue that some properties are due to their common origin in a conformal phase. Some of the scalar fields, including all higgsed ones, turn out to satisfy three-dimensional field equations similar to those of the singleton. Finally, we note that topologically gauged $ \mathcal{N} $ = 6 ABJ(M) theories have a similar, but more restricted, set of background solutions.