Critical solutions in topologically gauged N=8 CFTs in three dimensions

TL;DR

This paper explores special critical solutions in topologically gauged N=8 three-dimensional conformal field theories, analyzing their properties, spectrum, and symmetry breaking, revealing connections to singleton fields and similar solutions in N=6 theories.

Contribution

It identifies and characterizes critical background solutions in topologically gauged N=8 CFTs, including their spectrum and symmetry patterns, and relates them to known solutions in TMG and N=6 theories.

Findings

Identified critical solutions including Minkowski, AdS3, and null-warped AdS3.

Analyzed spectrum, symmetry breaking, and supermultiplet structures.

Found scalar fields satisfying singleton equations and connections to N=6 theories.

Abstract

In 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. These solutions solve the TMG equations (containing the parameters $\mu$ and $l$) for a certain set of values of $\mu l$ obtained by varying the number of scalar fields with a VEV. Apart from Minkowski, chiral round $AdS_3$ and null-warped $AdS_3$ (or Schr\"odinger(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 singleton field equations. Finally, we note that topologically gauged ${\mathcal N}=6$ ABJ(M) theories have a similar, but more restricted, set of background solutions.