Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points

TL;DR

<3-5 sentence high-level summary> This work analyzes the non-supersymmetric landscape within the SU(3)-invariant sector of 4D ${\cal N}=8$ gauged supergravity to test the stability of holographically relevant fixed points. By computing the full scalar mass spectrum at all non-trivial AdS critical points and linking the SU(4)^- instability to BF-bound violations, the authors demonstrate a BF-unstable non-supersymmetric vacuum whose instability is traced to 11D flux/metric perturbations via the Pope–Warner uplift. The instability is shown to arise from a primitive $(2,2)$ flux mode transforming in the ${\bf 20'}$ of ${\rm SU}(4)$, and the linear analysis extends to general SE$_7$/CY$_4$ settings, suggesting a broader obstruction to stable holographic superconductors in this sector. The paper also casts the SU(3)-invariant sector as a ${\cal N}=2$ theory with ${\rm U}(1)\times{\rm U}(1)$ gauging and one hypermultiplet, clarifying the geometric structure of the truncated model and its limitations for non-supersymmetric holography.

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.