AdS/CFT (Anti-de Sitter/Conformal Field Theory) is a conjectured duality between two seemingly different physical theories: a theory of gravity in Anti-de Sitter space (a type of curved spacetime) and a quantum field theory on the boundary of that space. This duality suggests that these two theories are actually equivalent, providing a way to understand the mysterious nature of quantum gravity in terms of a well-understood quantum field theory. String theory, which posits that all particles are actually tiny strings vibrating in higher-dimensional space, is the underlying framework for this duality.
In perturbative string theory, calculations are done by treating the strings as small perturbations on a flat background. However, this approach has limitations and is unable to capture the full complexity of the theory. Non-perturbative string theory, on the other hand, takes into account the full dynamics of the strings and allows for a better understanding of the theory at strong coupling. This is essential for understanding phenomena such as black holes and the Big Bang, which cannot be described by perturbative methods.
The AdS/CFT correspondence has been used to study black holes in both theories, providing insights into their properties and behavior. In particular, it has been shown that the entropy of a black hole in Anti-de Sitter space can be calculated using the dual conformal field theory on the boundary. This has opened up new avenues for understanding the information paradox and the connection between black holes and quantum entanglement.
At present, there is no direct experimental evidence for the AdS/CFT correspondence or for non-perturbative string theory. However, the duality has been tested through various mathematical and theoretical consistency checks, and it has been used to make predictions that have been confirmed by experiments in other areas of physics. Additionally, ongoing research in string theory and AdS/CFT may eventually lead to testable predictions that could be observed in future experiments.
One of the major challenges in this field is understanding how to apply the duality to real-world scenarios, such as in the study of condensed matter systems. Additionally, there are still many open questions and areas that need further exploration, such as the role of time and causality in the duality and how it can be extended to non-AdS spaces. Future research in this field will likely involve developing new mathematical techniques and collaborating with other areas of physics to gain a deeper understanding of the fundamental nature of our universe.