AdS/CFT duality exactness

Prove the exact equivalence between string theory with gravity on anti–de Sitter space and a conformal field theory defined on its boundary (the AdS/CFT duality), thereby establishing the conjectured non-perturbative holographic correspondence.

Background

The AdS/CFT correspondence (Maldacena conjecture) relates a gravitational string theory in AdS spacetime to a non-gravitational CFT on its boundary and is central to modern approaches to non-perturbative string theory and holography.

While the correspondence has strong evidence and extensive applications, it remains a conjecture as stated in the paper; a fully rigorous proof of exact equivalence would settle foundational questions about holography and non-perturbative string dynamics.

References

Additionally, there are attempts to construct a non-perturbative version of string theory; the most celebrated development being the AdS/CFT duality (also known as the Maldacena conjecture, after Maldacena 1998). This is a relationship—a conjectured exact equivalence—between a string theory featuring gravity, describing closed strings propagating on a spacetime (anti-de Sitter space (AdS)), known as the ‘bulk’, and a gauge theory without gravity (a conformal field theory (CFT)), defined on the boundary that contains the bulk spacetime.

— Why Do We Want a Theory of Quantum Gravity?  (2505.04858 - Crowther, 7 May 2025) in Section 2.1 (Background independence), paragraph introducing AdS/CFT

Whether the stronger condition is selected by the gravitational path integral, a superselection rule, or third-quantized sewing and dynamics remains open.

— A Third-Quantized Description of Spacetime Wormholes in AdS/CFT  (2608.23111 - Hirano, 24 Aug 2026) in Section 6, “Discussion and Outlook,” paragraph “CFT realizability and gravitational initial conditions”

A large class of warped AdS vacua in type II string theory are conjectured to be holographically dual to long quivers .

— Superconformal index of large N and long quivers  (2608.27933 - Akhond et al., 28 Aug 2026) in Section 1, Introduction and summary; Section 6, Outlook