Some interesting violations of the Breitenlohner-Freedman bound

TL;DR

The paper analyzes two classes of AdS vacua for stability under the Breitenlohner-Freedman bound: $AdS_5 \times T^{pq}$ and $AdS_3 \times S^7$ in Sugimoto's $USp(32)$ open string theory. Using explicit linearized fluctuations and the Lichnerowicz operator, it shows that all $T^{pq}$ with $p \neq q$ are BF-unstable (with $T^{11}$ marginally stable), and that the Sugimoto $AdS_3 \times S^7$ background hosts BF-violating tachyons. The work also maps the BF-saturating modes for $AdS_5 \times T^{11}$ to protected dimension-2 operators in the dual $\mathcal{N}=1$ SCFT, and discusses implications for AdS/CFT and the existence of heterotic duals in non-supersymmetric string theories. Overall, the results argue that non-supersymmetric AdS vacua generally lack consistent, unitary dual field theories.

Abstract

We demonstrate that AdS_5 x T^{pq} is unstable, in the sense of Breitenlohner and Freedman, for unequal p and q. This settles, negatively, the long-standing question of whether the T^{pq} manifolds for unequal p and q might correspond to non-supersymmetric fixed points of the renormalization group. We also show that the AdS_3 x S^7 vacuum of Sugimoto's USp(32) open string theory is unstable. This explains, at a heuristic level, the apparent absence of a heterotic string dual.