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

Abstract

In this paper we discuss some special (critical) background solutions that arise in topological gauged 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 T M G Lagrangian. Apart from Minkowski, chiral round AdS 3 and null-warped AdS 3 (or Schrödinger(z = 2)) we identify also a more exotic solution recently found in T M G 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 N = 6 ABJ(M) theories have a similar, but more restricted, set of background solutions.

Minimal N = 4 $$ \mathcal{N}=4 $$ topologically massive supergravity

“…By construction, the off-shell N = 4 topologically massive supergravity theory of [12] makes use of two compensators. However, in [20] the consistent system of dynamical equations was proposed for N = 4 topologically massive AdS supergravity with a single compensating hypermultiplet, following earlier work in [21][22][23] on ABJ(M) models. A peculiar feature of this model, like those considered in [21][22][23], is that it has no free parameter.…”

“…However, in [20] the consistent system of dynamical equations was proposed for N = 4 topologically massive AdS supergravity with a single compensating hypermultiplet, following earlier work in [21][22][23] on ABJ(M) models. A peculiar feature of this model, like those considered in [21][22][23], is that it has no free parameter. Consequently the dimensionless combination, µ , of mass µ and AdS radius takes a fixed value, µ = 1, as in chiral gravity [24].…”

“…In the on-shell construction of topologically gauged N = 6 and N = 8 ABJM type theories [21][22][23], a crucial role is played by a sixth order scalar potential. In the offshell approach, such a scalar potential is automatically generated upon elimination of the auxiliary fields, as was demonstrated in [58] where the N = 6 and N = 8 ABJM models were realised in N = 3 harmonic superspace.…”

“…Specifically, before imposing any gauge condition there is a term w 2 g ± in our actions and upon eliminating the auxiliary fields the term µ 2 g 3 ± is generated. This term plays a similar role as the sixth order polynomial in [21][22][23] in the sense that its coefficient is fixed by the equations of motion (in terms of the coupling coefficient of the conformal supergravity action) and the conformal coupling between the Einstein-Hilbert term and the O(2) multiplet. In this respect our model is akin to those of [21][22][23].…”

On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field

“…Another potentially interesting aspect arises if this higher spin theory can be generalized to contain the topologically gauged spin theories derived in [2,3,20]. Then perhaps the background solutions found in [20,21] could be lifted to the higher spin theory which could then provide information about how to write, e.g., an action also in AdS 3 , Schroedinger and the semi-flat Schroedinger geometries discussed in [21,22]. If this turns out to work it would give additional support for a "sequential AdS/CF T " phenomenon as suggested in [23] where Neumann boundary conditions and the associated dynamical conformal boundary theories play a crucial role.…”