The AdS/CFT correspondence is a groundbreaking idea in theoretical physics that connects two seemingly different frameworks: a gravitational theory in a higher-dimensional space and a quantum field theory without gravity on the boundary of that space.
Specifically, it posits that a string theory (or gravity theory) in anti-de Sitter space (AdS)—a curved spacetime with constant negative curvature—is exactly equivalent to a conformal field theory (CFT) defined on the boundary of that space. This means every physical process in the bulk gravitational theory has a counterpart in the boundary quantum theory, and vice versa.
This duality provides a powerful tool for understanding quantum gravity, since it translates difficult problems in gravitational physics into more manageable quantum field theory calculations. It also allows physicists to explore strongly coupled systems—like those in nuclear physics or condensed matter—using geometric and gravitational concepts.
The AdS/CFT correspondence embodies the holographic principle, revealing that gravity and spacetime may emerge from more fundamental quantum systems defined on lower-dimensional boundaries.