Supergravity instabilities of non-supersymmetric quantum critical points

Motivated by the recent use of certain consistent truncations of M -theory to study condensed matter physics using holographic techniques, we study the SU (3)-invariant sector of four-dimensional, gauged supergravity and compute the complete scalar spectrum at each of the five non-trivial critical points. We demonstrate that the smaller SU (4) − sector is equivalent to a consistent truncation studied recently by various authors and find that the critical point in this sector, which has been proposed as the ground state of a holographic superconductor, is unstable due to a family of scalars that violate the Breitenlohner–Freedman bound. We also derive the origin of this instability in 11 dimensions and comment on the generalization to other embeddings of this critical point which involve arbitrary Sasaki–Einstein seven manifolds. In the spirit of a resurging interest in consistent truncations, we present a formal treatment of the SU (3)-invariant sector as a U (1) × U (1) gauged supergravity theory coupled to one hypermultiplet.