The AdS/CFT correspondence, also known as the gauge/gravity duality or holographic principle, is a profound result in theoretical physics that establishes a connection between certain quantum field theories (QFTs) and string theories.
The correspondence was initially proposed by Juan Maldacena in 1997 and has since been the subject of extensive research and development. It relates a quantum field theory living on the boundary of a spacetime region known as Anti-de Sitter space (AdS) to a string theory living in the higher-dimensional spacetime called the bulk.
Specifically, the AdS/CFT correspondence states that a strongly interacting QFT in d dimensions can be described by a weakly coupled gravitational theory in d+1 dimensions. More precisely, the gravitational theory in the bulk is a string theory that exhibits gravity, while the QFT living on the boundary of the bulk is a gauge theory without gravity.
The correspondence provides a powerful tool for studying strongly coupled gauge theories. In many cases, calculating quantities in a strongly interacting QFT is extremely challenging using conventional techniques. However, by mapping the QFT to a dual weakly coupled gravitational theory in higher dimensions, physicists can exploit the power of string theory and gravitational methods to gain insights into the strongly coupled QFT.
The AdS/CFT correspondence has led to several significant advancements in our understanding of both QFTs and string theories. It has provided insights into the behavior of strongly coupled systems, the dynamics of black holes, and the emergence of spacetime from underlying quantum degrees of freedom.
Furthermore, the correspondence has also provided a bridge between seemingly unrelated areas of physics. It has helped establish connections between condensed matter physics and gravity, leading to the development of new techniques and ideas in both fields.
In summary, the AdS/CFT correspondence plays a crucial role in deepening our understanding of the relationship between quantum field theories and string theories. It allows us to explore the behavior of strongly coupled systems using gravitational techniques and has opened up new avenues for research and discovery in theoretical physics.