Editing AdS/CFT correspondence (section)

=== Quantum gravity and strings ===

{{Main|Quantum gravity| String theory}}

Current understanding of [[gravity]] is based on [[Albert Einstein]]'s [[general theory of relativity]].{{refn|A standard textbook on general relativity is {{harvnb|Wald|1984}}.}} Formulated in 1915, general relativity explains gravity in terms of the geometry of space and time, or [[spacetime]]. It is formulated in the language of [[classical physics]]{{sfn|ps=|Maldacena|2005|p=58}} that was developed by physicists such as [[Isaac Newton]] and [[James Clerk Maxwell]]. The other nongravitational forces are explained in the framework of [[quantum mechanics]]. Developed in the first half of the twentieth century by a number of different physicists, quantum mechanics provides a radically different way of describing physical phenomena based on probability.{{sfn|ps=|Griffiths|2004}}

[[Quantum gravity]] is the branch of physics that seeks to describe gravity using the principles of quantum mechanics. Currently, a popular approach to quantum gravity is [[string theory]],{{sfn|Maldacena|2005|p=62}} which models [[elementary particle]]s not as zero-dimensional points but as one-dimensional objects called [[string (physics)|strings]]. In the AdS/CFT correspondence, one typically considers theories of quantum gravity derived from string theory or its modern extension, [[M-theory]].{{refn|See subsection ''{{slink|#Examples of the correspondence}}''. For examples that do not involve string theory or M-theory, see section ''{{slink|#Generalizations}}''.}}

In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there is one dimension of time. Thus, in the language of modern physics, one says that spacetime is four-dimensional.{{sfn|ps=|Wald|1984|p=4}} One peculiar feature of string theory and M-theory is that these theories require [[extra dimensions]] of spacetime for their mathematical consistency: in string theory spacetime is ten-dimensional, while in M-theory it is eleven-dimensional.{{sfn|ps=|Zwiebach|2009|p=8}} The quantum gravity theories appearing in the AdS/CFT correspondence are typically obtained from string and M-theory by a process known as [[compactification (physics)|compactification]]. This produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are "curled up" into circles.{{sfn|ps=|Zwiebach|2009|pp=7–8}}

A standard analogy for compactification is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length, but as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions.{{refn|This analogy is used for example in {{harvnb|Greene|2000|p=186}}.}}