AdS–CFT correspondence

Establish the duality between quantum gravity in asymptotically (locally) Anti-de Sitter spacetime in n+1 dimensions and an n-dimensional conformal field theory by proving the equivalence of states, quantities, and dynamics (e.g., via equality of the CFT partition function and the gravitational path integral).

Background

The authors present AdS-CFT as a central example of gauge–gravity duality that, if true, furnishes a non-perturbative definition of quantum gravity in AdS spacetimes via a boundary CFT. They emphasize its role as a quantum duality where semiclassical limits differ across sides.

They explicitly introduce AdS-CFT as a conjectured duality, framing the equivalence in terms of partition functions and path integrals, and note that establishing this equivalence would secure the duality’s formal features required by their Schema.

References

AdS-CFT: the (conjectured) duality between quantum gravity in (asymptotically, locally) Anti de Sitter (AdS) spacetime in $n+1$ dimensions, and a conformal quantum field theory (CFT) in $n$ dimensions.

— Dualities in Physics  (2509.15866 - Haro et al., 19 Sep 2025) in Section 4.4 AdS-CFT and Bulk Reconstruction

Second, the program of gauge-gravity duality aims to extend the case of AdS/CFT to more physically meaningful field theories, but the correspondence itself, in its most illuminating example, is only conjectured rather than proven.

— Condensates: A Bridge to Quantum Gravity  (2609.28789 - Nicolini, 23 Sep 2026) in Section 3, “Condensed Matter as a Laboratory”

They specify boundary states and pairings for localized one-particle excitations within the proposed correspondence in eq.\,eq:hilbert-space-goal, while leaving the completion of the Hilbert spaces and the interacting correspondence open.

— Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography  (2610.07548 - Hao et al., 6 Oct 2026) in Introduction, paragraph beginning “These constructions show how boundary descendants”