# AdS/CFT correspondence

**The duality represents a major advance in the understanding of string theory and quantum gravity. Current understanding of gravity is based on Albert Einstein’s general theory of relativity. The correspondence has been used to study many aspects of nuclear and condensed matter physics by translating problems in those subjects into more mathematically tractable problems in string theory.**

### About AdS/CFT correspondence in brief

In theoretical physics, the anti-de Sitterconformal field theory correspondence, sometimes called Maldacena duality or gaugegravity duality, is a conjectured relationship. The duality represents a major advance in the understanding of string theory and quantum gravity. Current understanding of gravity is based on Albert Einstein’s general theory of relativity. In the AdSCFT correspondence, one typically considers theories of quantum gravity derived from string theory or its modern extension, M-theory. This is a particularly symmetric type of quantum field theory. Such theories are often studied in the context ofstring theory, where they are associated with the surface swept out by a string propagating through spacetime. They model systems at a thermodynamic critical point where they model particles at a critical critical point in the universe. The correspondence has been used to study many aspects of nuclear and condensed matter physics by translating problems in those subjects into more mathematically tractable problems in string theory. It is the most successful realization of the holographic principle, an idea in quantum gravity originally proposed by Gerard ‘t Hooft and promoted by Leonard Susskind. It also provides a powerful toolkit for studying strongly coupled quantum field theories, such as the Yang–Mills theories that describe elementary particles. It has become the most highly cited article in the field of high energy physics, reaching almost 20,000 citations by 2020. It was first proposed by Juan Maldaceno in late 1997. By 2015, Maldacencia’s article had over 10,000 citation, becoming the mosthighly cited article.

The quantum gravity theories appearing in the correspondence are typically obtained from string and M- theory by a process known as compactification. This produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are curled up into circles. In everyday life, there are three familiar dimensions of space, and there is one dimension of time, Thus, in the language of modern physics, one says that spacetime is four-dimensional. One peculiar feature of string 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 and so on. This means that the spacetime described in this correspondence is described in terms of a certain vacuum equation called Einstein’s anti- de Sitter space. In quantum gravity, one considers one-dimensional string theory on an anti-De Sitter spacetime on one side of the correspondence, and one-dimension string theory on the other side of this correspondence. In this way, the two theories can be viewed in different ways, depending on the type of field theory being used. The AdSC FT correspondence is used to model certain types of quantumgravity theories called quasiparticles, which are used throughout condensed matter Physics and also also in nuclear physics. It provides a non-perturbative formulation of string theories with certain boundary conditions.

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