Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points

TL;DR

This paper analyzes the stability of non-supersymmetric critical points in a supergravity model relevant to holographic condensed matter, revealing instabilities and providing a detailed spectrum analysis.

Contribution

It computes the complete scalar spectrum at critical points in SU(3)-invariant supergravity and identifies instabilities related to scalar violations of the Breitenlohner-Freedman bound.

Findings

The SU(4)^- sector critical point is unstable due to scalar violations of the BF bound.

The origin of the instability is traced back to eleven-dimensional supergravity.

The SU(3)-invariant sector is formulated as a U(1)xU(1) gauged N=2 supergravity with a hypermultiplet.

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 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)xU(1) gauged N=2 supergravity theory coupled to one hypermultiplet.