Editing AdS/CFT correspondence (section)

=== Examples of the correspondence ===

Following Maldacena's insight in 1997, theorists have discovered many different realizations of the AdS/CFT correspondence. These relate various conformal field theories to compactifications of string theory and M-theory in various numbers of dimensions. The theories involved are generally not viable models of the real world, but they have certain features, such as their particle content or high degree of symmetry, which make them useful for solving problems in quantum field theory and quantum gravity.{{refn|The known realizations of AdS/CFT typically involve unphysical numbers of spacetime dimensions and unphysical supersymmetries.}}

The most famous example of the AdS/CFT correspondence states that [[type IIB string theory]] on the [[product space]] {{nowrap|AdS<sub>5</sub> × ''S''<sup>5</sup>}} is equivalent to [[N = 4 supersymmetric Yang–Mills theory|''N'' = 4 supersymmetric Yang–Mills theory]] on the four-dimensional boundary.{{refn|This example is the main subject of the three pioneering articles on AdS/CFT: {{harvnb|Maldacena|1998}}; {{harvnb|Gubser|Klebanov|Polyakov|1998}}; and {{harvnb|Witten|1998}}.}} In this example, the spacetime on which the gravitational theory lives is effectively five-dimensional (hence the notation AdS<sub>5</sub>), and there are five additional [[compact dimension]]s (encoded by the ''S''<sup>5</sup> factor). In the real world, spacetime is four-dimensional, at least macroscopically, so this version of the correspondence does not provide a realistic model of gravity. Likewise, the dual theory is not a viable model of any real-world system as it assumes a large amount of [[supersymmetry]]. Nevertheless, as explained below, this boundary theory shares some features in common with [[quantum chromodynamics]], the fundamental theory of the [[strong force]]. It describes particles similar to the [[gluon]]s of quantum chromodynamics together with certain [[fermion]]s.{{sfn|Maldacena|2005|p=62}} As a result, it has found applications in [[nuclear physics]], particularly in the study of the [[quark–gluon plasma]].{{sfn|ps=|Merali|2011|p=303}}{{sfn|ps=|Kovtun|Son|Starinets|2005}}

Another realization of the correspondence states that M-theory on {{nowrap|AdS<sub>7</sub> × ''S''<sup>4</sup>}} is equivalent to the so-called [[6D (2,0) superconformal field theory|(2,0)-theory]] in six dimensions.{{sfn|ps=|Maldacena|1998|loc=The pre-print was submitted in 1997 and published on January 1, 1998.}} In this example, the spacetime of the gravitational theory is effectively seven-dimensional. The existence of the (2,0)-theory that appears on one side of the duality is predicted by the classification of [[super conformal field theory|superconformal field theories]]. It is still poorly understood because it is a quantum mechanical theory without a [[classical limit]].{{refn|For a review of the (2,0)-theory, see {{harvnb|Moore|2012}}.}} Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for a variety of reasons, both physical and mathematical.{{refn|See {{harvnb|Moore|2012}} and {{harvnb|Alday|Gaiotto|Tachikawa|2010}}.}}

Yet another realization of the correspondence states that M-theory on {{nowrap|AdS<sub>4</sub> × ''S''<sup>7</sup>}} is equivalent to the [[ABJM superconformal field theory]] in three dimensions.{{sfn|ps=|Aharony|Bergman|Jafferis|Maldacena|2008}} Here the gravitational theory has four noncompact dimensions, so this version of the correspondence provides a somewhat more realistic description of gravity.{{sfn|ps=|Aharony|Bergman|Jafferis|Maldacena|2008|loc=sec. 1}}