Editing AdS/CFT correspondence (section)

=== A non-perturbative formulation of string theory ===

[[Image:World lines and world sheet.svg|right|thumb|upright=1.2|Interaction in the quantum world: [[world line]]s of point-like [[particles]] or a [[world sheet]] swept up by closed [[string (physics)|strings]] in string theory.]]

In quantum field theory, one typically computes the probabilities of various physical events using the techniques of [[perturbation theory]]. Developed by [[Richard Feynman]] and others in the first half of the twentieth century, perturbative quantum field theory uses special diagrams called [[Feynman diagram]]s to organize computations. One imagines that these diagrams depict the paths of point-like particles and their interactions.{{refn|A standard textbook introducing the formalism of Feynman diagrams is {{harvnb|Peskin|Schroeder|1995}}.}} Although this formalism is extremely useful for making predictions, these predictions are only possible when the strength of the interactions, the [[coupling constant]], is small enough to reliably describe the theory as being close to a theory [[free field|without interactions]].{{sfn|ps=|Zee|2010|p=43}}

The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-dimensional objects called strings. The interaction of strings is most straightforwardly defined by generalizing the perturbation theory used in ordinary quantum field theory. At the level of Feynman diagrams, this means replacing the one-dimensional diagram representing the path of a point particle by a two-dimensional surface representing the motion of a string. Unlike in quantum field theory, string theory does not yet have a full non-perturbative definition, so many of the theoretical questions that physicists would like to answer remain out of reach.{{sfn|ps=|Zwiebach|2009|p=12}}

The problem of developing a non-perturbative formulation of string theory was one of the original motivations for studying the AdS/CFT correspondence.{{sfn|ps=|Maldacena|1998|loc=sec. 6}} As explained above, the correspondence provides several examples of quantum field theories that are equivalent to string theory on anti-de&nbsp;Sitter space. One can alternatively view this correspondence as providing a ''definition'' of string theory in the special case where the gravitational field is asymptotically anti-de&nbsp;Sitter (that is, when the gravitational field resembles that of anti-de&nbsp;Sitter space at spatial infinity). Physically interesting quantities in string theory are defined in terms of quantities in the dual quantum field theory.{{sfn|ps=|Maldacena|2005|p=61}}