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.