Some interesting violations of the Breitenlohner-Freedman bound

TL;DR

This paper investigates the stability of certain anti-de Sitter spaces, revealing instabilities in specific configurations and providing insights into their implications for string theory dualities.

Contribution

It demonstrates the instability of AdS_5 x T^{pq} for unequal p and q, and shows the instability of the AdS_3 x S^7 vacuum in Sugimoto's string theory, clarifying longstanding questions.

Findings

AdS_5 x T^{pq} is unstable for p ≠ q

AdS_3 x S^7 vacuum is unstable in Sugimoto's theory

No stable non-supersymmetric fixed points for these configurations

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.