The AdS/CFT correspondence which was formulated nearly a decade ago, has revolutionized our way of thinking about quantum gravity. The correspondence in its strong form basically states that one can encode the dynamics of string theory (or quantum gravity) in asymptotically AdS spacetimes is dual to a field theory without gravity. The most famous example of this is the relation between string theory on AdS55 × S5S5 and a particular supersymmetric gauge theory called =4N4 super Yang-Mills.
As it relates quantum gravity in a particular background spacetime to a field theory, the correspondence provides a remarkable window into understanding gravitational dynamics; all one needs to do is to address the analogous question in the field theory. While the dictionary between the field theory and gravity has been developed to a certain extent over the last decade, there still remain many interesting issues that are to be explored.
Furthermore, like all dualities the gravitational description can be used to elicit the behaviour of gauge dynamics: typically strongly coupled dynamics for which there are few theoretical tools. In recent times there is renewed interest in applying these ideas in the context of QCD, and in particular to better understand transport properties of QCD matter at strong coupling. Remarkably, some of the results obtained from the AdS/QCD analysis are quite close to observed properties of QCD matter. Furthermore, there is much activity in recent times in trying to use AdS/CFT methods to learn about strongly coupled condensed matter systems.
There are a couple of articles for non-experts giving an overview of some of the fascinating aspects of AdS/CFT:
- Gauge/gravity duality by Gary Horowitz and Joe Polchinski: gr-qc/0602037
- Comments on black holes in string theory by Gary Horowitz: hep-th/9910082
For AdS/CFT itself there is a reasonably comprehensive technical review:
- Large N field theories, string theory and gravity, by Ofer Aharony, Steve Gubser, Juan Maldacena, Hirosi Ooguri and Yaron Oz: hep-th/9905111
and the original references developing the subject:
- The Large N Limit of Superconformal Field Theories and Supergravity, by Juan Maldacena: hep-th/9711200
- Anti-de Sitter space and holography by Edward Witten: hep-th/9802150
- Gauge theory correlators from noncritical string theory by Steve Gubser, Igor Klebanov and Alexander Polyakov: hep-th/9802109
A more modern review with emphasis on GR aspects is
- The AdS/CFT correspondence, by Veronika Hubeny: hep-th/1501.00007
Videos and lecture notes
- The video of an introductory set of lectures on the AdS/CFT correspondence given by me at the Newton Institute workshop, Gauge fields and strings in 2007 can be found at Newton Institute Lectures.
- A more recent set of lectures at the LACES school in Galileo Galilei Institute, Florence can be found at Gauge/gravity duality and holography.
- A partial set of lecture notes based on the above can be found here: The AdS/CFT correspondence.
- I recently co-authored a book on holographic entanglement entropy with Tadashi Takayanagi. The arXiv version at arxiv:1609.01287 include many of the chapters. The book itself can be found online, eg., Amazon link.