Identify gravitational saddles needed to exclude finely tuned TFTs

Determine the specific bulk gravitational saddle points in asymptotically AdS spacetimes that are required to rule out topological field theories which trivialize on both thermal AdS and AdS–Schwarzschild saddles yet remain non-trivial on more complicated saddles, thereby extending the non-decoupling contradiction to these fine-tuned cases.

Background

The paper argues that putatively decoupled topological field theories (TFTs) in AdS gravity cannot remain independent of Newton’s constant because bulk Euclidean path integrals sum over topologically distinct saddles whose dominance changes across the Hawking–Page transition. This induces a mismatch with boundary correlators that are claimed to be independent of the large-N sector, implying no truly decoupled TFTs.

A potential loophole is raised: a finely tuned TFT might yield trivial correlators on both canonical saddles (thermal AdS and AdS–Schwarzschild), while staying non-trivial on other, more complicated saddles. The authors suggest that phase transitions involving these more complicated saddles should produce similar contradictions but leave the precise identification of such saddles for future work. They note that such TFTs would display pathological linking properties, yet a concrete exclusion requires determining the relevant saddle points.