Editing AdS/CFT correspondence (section)

== History and development ==

[[File:Gerard 't Hooft.jpg|right|thumb|upright=0.6|[[Gerard 't Hooft]] obtained results related to the {{nowrap|AdS/CFT}} correspondence in the 1970s by studying analogies between [[string theory]] and [[nuclear physics]].]]

=== String theory and nuclear physics ===

{{Main|History of string theory|1/N expansion}}

The discovery of the AdS/CFT correspondence in late 1997 was the culmination of a long history of efforts to relate string theory to nuclear physics.{{sfn|ps=|Zwiebach|2009|p=525}} In fact, string theory was originally developed during the late 1960s and early 1970s as a theory of [[hadron]]s, the [[subatomic particle]]s like the [[proton]] and [[neutron]] that are held together by the [[strong nuclear force]]. The idea was that each of these particles could be viewed as a different oscillation mode of a string. In the late 1960s, experimentalists had found that hadrons fall into families called [[Regge trajectories]] with squared [[energy]] proportional to [[angular momentum]], and theorists showed that this relationship emerges naturally from the physics of a rotating [[Principle of relativity|relativistic]] string.{{sfn|ps=|Aharony|Bergman|Jafferis|Maldacena|2008|loc=sec. 1.1}}

On the other hand, attempts to model hadrons as strings faced serious problems. One problem was that string theory includes a [[mass]]less [[Spin (physics)|spin-2]] particle whereas no such particle appears in the physics of hadrons.{{sfn|ps=|Zwiebach|2009|p=525}}  Such a particle would mediate a force with the properties of gravity. In 1974, [[Joël Scherk]] and [[John Henry Schwarz|John Schwarz]] suggested that string theory was therefore not a theory of nuclear physics as many theorists had thought but instead a theory of quantum gravity.{{sfn|ps=|Scherk|Schwarz|1974}} At the same time, it was realized that hadrons are actually made of quarks, and the string theory approach was abandoned in favor of quantum chromodynamics.{{sfn|ps=|Zwiebach|2009|p=525}}

In quantum chromodynamics, quarks have a kind of [[charge (physics)|charge]] that comes in three varieties called [[color charge|colors]]. In a paper from 1974, [[Gerard 't Hooft]] studied the relationship between string theory and nuclear physics from another point of view by considering theories similar to quantum chromodynamics, where the number of colors is some arbitrary number ''N'', rather than three. In this article, 't Hooft considered a certain limit where ''N'' tends to infinity and argued that in this limit certain calculations in quantum field theory resemble calculations in string theory.{{sfn|ps=|'t Hooft|1974}}

=== Black holes and holography ===
[[Image:Stephen Hawking.StarChild.jpg|thumb|left|upright=0.6|[[Stephen Hawking]] predicted in 1975 that [[black hole]]s emit [[Hawking radiation|radiation]] due to quantum effects.]]

{{Main|Black hole information paradox|Thorne–Hawking–Preskill bet|Holographic principle}}

In 1975, Stephen Hawking published a calculation that suggested that black holes are not completely black but emit a dim radiation due to quantum effects near the event horizon.{{sfn|ps=|Hawking|1975}} This work extended previous results of [[Jacob Bekenstein]] who had suggested that black holes have a well-defined entropy.{{sfn|ps=|Bekenstein|1973}} At first, Hawking's result appeared to contradict one of the main postulates of quantum mechanics, namely the unitarity of time evolution. Intuitively, the unitarity postulate says that quantum mechanical systems do not destroy information as they evolve from one state to another. For this reason, the apparent contradiction came to be known as the black hole information paradox.{{sfn|ps=|Susskind|2008}}

[[File:LeonardSusskindStanford2009 cropped.jpg|thumb|upright=0.6|[[Leonard Susskind]] made early contributions to the idea of [[holography]] in [[quantum gravity]].]]

Later, in 1993, Gerard 't Hooft wrote a speculative paper on quantum gravity in which he revisited Hawking's work on [[black hole thermodynamics]], concluding that the total number of [[degree of freedom|degrees of freedom]] in a region of spacetime surrounding a black hole is proportional to the [[surface area]] of the horizon.{{sfn|ps=|'t Hooft|1993}} This idea was promoted by [[Leonard Susskind]] and is now known as the [[holographic principle]].{{sfn|ps=|Susskind|1995}} The holographic principle and its realization in string theory through the AdS/CFT correspondence have helped elucidate the mysteries of black holes suggested by Hawking's work and are believed to provide a resolution of the black hole information paradox.{{sfn|ps=|Maldacena|2005|p=63}} In 2004, Hawking conceded that black holes do not violate quantum mechanics,{{sfn|ps=|Susskind|2008|p=444}} and he suggested a concrete mechanism by which they might preserve information.{{sfn|ps=|Hawking|2005}}

=== Maldacena's paper ===
[[Image:JuanMaldacena.jpg|thumb|upright=0.6|[[Juan Maldacena]] first proposed the AdS/CFT correspondence in late 1997.]]

On January 1, 1998, [[Juan Maldacena]] published a landmark paper that initiated the study of AdS/CFT.{{sfn|ps=|Maldacena|1998|loc=The pre-print was submitted in 1997 and published on January 1, 1998.}} According to [[Alexander Markovich Polyakov]], "[Maldacena's] work opened the flood gates."{{sfn|ps=|Polyakov|2008|p=6}} The conjecture immediately excited great interest in the string theory community{{sfn|ps=|Maldacena|2005|p=63}} and was considered in a paper by [[Steven Gubser]], [[Igor Klebanov]] and Polyakov,{{sfn|ps=|Gubser|Klebanov|Polyakov|1998}} and another paper of [[Edward Witten]].{{sfn|ps=|Witten|1998}} These papers made Maldacena's conjecture more precise and showed that the conformal field theory appearing in the correspondence lives on the boundary of anti-de&nbsp;Sitter space.{{sfn|ps=|Polyakov|2008|p=6}}

One special case of Maldacena's proposal says that {{nowrap|1=''N'' = 4}} super Yang–Mills theory, a [[gauge theory]] similar in some ways to quantum chromodynamics, is equivalent to string theory in five-dimensional anti-de&nbsp;Sitter space.{{sfn|ps=|Aharony|Bergman|Jafferis|Maldacena|2008}} This result helped clarify the earlier work of 't Hooft on the relationship between string theory and quantum chromodynamics, taking string theory back to its roots as a theory of nuclear physics.{{sfn|ps=|Aharony|Bergman|Jafferis|Maldacena|2008|loc=sec. 1.1}} Maldacena's results also provided a concrete realization of the holographic principle with important implications for quantum gravity and black hole physics.{{sfn|ps=|de Haro|Dieks|'t Hooft|Verlinde|2013|p=2}} By the year 2015, Maldacena's paper had become the most highly cited paper in [[high energy physics]] with over 10,000 citations.{{refn|name="inspire"}} These subsequent articles have provided considerable evidence that the correspondence is correct, although so far it has not been [[Mathematical proof|rigorously proved]].{{sfn|ps=|Maldacena|2005|p=63}}{{sfn|ps=|Cowen|2013}}