Supergravity instabilities of non-supersymmetric quantum critical points

Abstract

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, N = 8 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 eleven dimensions and comment on the generalization to other embeddings of this critical point which involve arbitrary SasakiEinstein 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 N = 2 supergravity theory coupled to one hypermultiplet.

Emergent Schrödinger geometries from mass-deformed CFT

“…An instability was reported for a solution in the skew-whiffed truncation with nonzero values of the charged field [34]. Although the solution we discussed is more complicated than the AdS solution studied there, at least studies of the IR solution (2.23) would be doable and worthwhile.…”

Consistent N = 8 $$ \mathcal{N}=8 $$ truncation of massive IIA on S 6

“…The mass spectra above the AdS vacua in this overlapping sector contain the common modes at the bottom of the KK towers. For example, D = 4 N = 8 electrically gauged SO(8) supergravity [1] and the universal N = 2 (skew-whiffed) Sasaki-Einstein truncation of D = 11 supergravity on S 7 [35] overlap [46] in the SU(4) − -invariant sector of the N = 8 theory. Likewise, D = 5 SO(6)-gauged supergravity [3] and the universal N = 4 Sasaki-Einstein truncation of type IIB on S 5 [37,38] overlap [47] in the SU(3)-invariant sector of the N = 8 theory.…”

Warped Ricci-flat reductions

“…Indeed, it is worth observing that we can also truncate out δϕ i , in which case the instability would not be observed. This is a pretty trivial example of the hidden instabilities noted in a higher-dimensional context in [18].…”

“…We explicitly construct a KK reduction Ansatz and note that the lower-dimensional theory one gets is five-dimensional U(1) 3 gauged supergravity [17] on the nose. Importantly, this observation guarantees stability within our truncation, though of course instabilities can arise from modes that are truncated out [18]. In the absence of warping, the (A)dS 5 vacuum becomes a Minkowski vacuum and one can compactify the internal space to get the usual KK reduction to ungauged supergravity on a Calabi-Yau manifold.…”

“…However, this does not preclude the possibility that instabilities arise from modes we have truncated out, for example see [18]. Within this restricted scope, we will explicitly show that lowerdimensional Freund-Rubin type solutions with AdS 3 factors enjoy greater stability than higher-dimensional vacua in the truncated theory.…”