AdS/CFT correspondence

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For the relation of the AdS/CFT correspondence to the general context of string theory, see gauge-gravity duality.

In physics, the AdS/CFT correspondence (anti-De-Sitter space/conformal field theory correspondence), sometimes called the Maldacena duality, is the conjectured equivalence between a string theory defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by at least one. The name suggests that the first space is the product of anti de Sitter space (AdS) with some closed manifold like sphere, orbifold, or noncommutative space, and that the quantum field theory is a conformal field theory (CFT). However, the conjectured equivalence is more general, and is therefore sometimes termed gauge / gravity duality.

An example is the duality between Type IIB string theory defined on AdS₅ × S⁵ space (a product of five dimensional AdS space with a five dimensional sphere) and a supersymmetric N=4 Yang-Mills gauge theory (which is a conformal field theory) defined on the 4-dimensional boundary of AdS₅. It is the most successful realization of the holographic principle, a speculative idea about quantum gravity originally proposed by Gerard 't Hooft and improved and promoted by Leonard Susskind. Although it remains unproven, the conjecture has been mathematically tested in many cases (i.e. various calculations performed on both sides, which are conjectured to be equivalent, indeed yield equivalent results).

The AdS/CFT correspondence was originally proposed by Juan Maldacena in late 1997. A more precise statement of the correspondence was soon given in articles by Gubser, Klebanov, and Polyakov, and by Edward Witten. The correspondence has also been generalized and applied to many other (non-AdS) backgrounds and their dual (non-conformal) theories. In about five years, Maldacena's article had 3000 citations and became one of the most obvious conceptual breakthroughs in theoretical physics of the 1990s, providing stark new insight into both quantum gravity and QCD.