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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.

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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